Portfolio-Optimization.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'C:\\\\Users\\\\Lenovo\\\\Desktop\\\\Portfolio-Optimization-Using-Markowitz-Model'"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "os.getcwd()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "number_of_assets=5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "number_of_observations=4000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "return_vec= np.random.randn(number_of_assets, number_of_observations)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.25926575,  0.03468524, -1.27949175, ...,  0.45194392,\n",
       "         0.75410883,  0.1502216 ],\n",
       "       [ 1.20995753, -1.50678004, -0.60224442, ..., -0.83153544,\n",
       "        -0.07686055,  0.04270244],\n",
       "       [ 1.37731859, -0.36596929,  1.18287955, ..., -0.195933  ,\n",
       "         0.61668928, -0.41574978],\n",
       "       [ 0.30312251,  1.27530486,  1.48088105, ...,  0.4611618 ,\n",
       "        -0.22605006, -0.98518136],\n",
       "       [ 0.85175433, -0.54759924,  1.64188757, ..., -1.46390888,\n",
       "         1.19958159, -0.47802237]])"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "return_vec"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rand_weights(n):\n",
    "    k = np.random.rand(n)\n",
    "    return (k)/(sum(k))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "def random_portfolio(returns):\n",
    "    p = np.asmatrix(np.mean(returns, axis=1))\n",
    "    w = np.asmatrix(rand_weights(returns.shape[0]))\n",
    "    C = np.asmatrix(np.cov(returns))\n",
    "    mu = w * p.T\n",
    "    sigma = np.sqrt(w * C * w.T)\n",
    "    return mu, sigma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "number_of_portfolio=1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "while True:\n",
    "    means, stds = np.column_stack([\n",
    "        random_portfolio(return_vec) \n",
    "        for _ in range(number_of_portfolio)\n",
    "        ])\n",
    "    if stds.all() <= 2:\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
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       "       [-1.54922836e-02],\n",
       "       [-2.87816993e-03]])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "means"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "       [0.50237558],\n",
       "       [0.52443677],\n",
       "       [0.47230713],\n",
       "       [0.52777511],\n",
       "       [0.49490589],\n",
       "       [0.47470484],\n",
       "       [0.48657449],\n",
       "       [0.48683367],\n",
       "       [0.47595164],\n",
       "       [0.52329339],\n",
       "       [0.50985359],\n",
       "       [0.57021098],\n",
       "       [0.46324671],\n",
       "       [0.5207818 ],\n",
       "       [0.46290929],\n",
       "       [0.46967884],\n",
       "       [0.57709043],\n",
       "       [0.46223016],\n",
       "       [0.53161199],\n",
       "       [0.59601949],\n",
       "       [0.46674865]])"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1000"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(stds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1000"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(means)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [],
   "source": [
    "import plotly.graph_objects as go"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
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        "plotlyServerURL": "https://plot.ly"
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       "                            \n",
       "var gd = document.getElementById('4c4ac98a-48f3-4bfe-8fc0-c2754bd7052d');\n",
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       "            console.log([gd, 'removed!']);\n",
       "            Plotly.purge(gd);\n",
       "            observer.disconnect();\n",
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       "\n",
       "// Listen for the removal of the full notebook cells\n",
       "var notebookContainer = gd.closest('#notebook-container');\n",
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = go.Figure()\n",
    "fig.update_layout(xaxis_title='Standard Deviation', \n",
    "                  yaxis_title='Mean')\n",
    "fig.add_trace(go.Scatter(x=stds.flatten(), y=means.flatten(),mode='markers'))\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "import cvxopt as opt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "from cvxopt import blas, solvers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def optimize(returns):\n",
    "    n = len(returns)\n",
    "    returns = np.asmatrix(returns)\n",
    "    N = 100\n",
    "    mus = [10**(5.0 * t/N - 1.0) for t in range(N)]\n",
    "    S = opt.matrix(np.cov(returns))\n",
    "    pbar = opt.matrix(np.mean(returns, axis=1))\n",
    "    G = -opt.matrix(np.eye(n))   # negative n x n identity matrix\n",
    "    h = opt.matrix(0.0, (n ,1))\n",
    "    A = opt.matrix(1.0, (1, n))\n",
    "    b = opt.matrix(1.0)\n",
    "    \n",
    "    portfolios = [solvers.qp(mu*S, -pbar, G, h, A, b)['x'] for mu in mus]\n",
    "    returns = [blas.dot(pbar, x) for x in portfolios]\n",
    "    risks = [np.sqrt(blas.dot(x, S*x)) for x in portfolios]\n",
    "    m1 = np.polyfit(returns, risks, 2)\n",
    "    x1 = np.sqrt(m1[2] / m1[0])\n",
    "    wt = solvers.qp(opt.matrix(x1 * S), -pbar, G, h, A, b)['x']\n",
    "    \n",
    "    return np.asarray(wt), returns, risks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  6.3958e-03 -1.0189e+00  1e+00  1e-16  3e+00\n",
      " 1:  5.6406e-03 -2.7970e-02  3e-02  2e-16  9e-02\n",
      " 2: -1.1791e-03 -5.7707e-03  5e-03  2e-16  2e-17\n",
      " 3: -2.5655e-03 -2.8868e-03  3e-04  2e-16  5e-18\n",
      " 4: -2.7066e-03 -2.7141e-03  7e-06  2e-16  6e-18\n",
      " 5: -2.7084e-03 -2.7085e-03  8e-08  2e-16  1e-17\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  7.6590e-03 -1.0174e+00  1e+00  0e+00  3e+00\n",
      " 1:  6.9236e-03 -2.6309e-02  3e-02  9e-17  9e-02\n",
      " 2:  7.0994e-04 -3.4532e-03  4e-03  2e-16  2e-17\n",
      " 3: -5.7186e-04 -8.6207e-04  3e-04  1e-16  8e-18\n",
      " 4: -7.2058e-04 -7.2475e-04  4e-06  1e-16  1e-17\n",
      " 5: -7.2275e-04 -7.2279e-04  4e-08  1e-16  8e-18\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  9.0750e-03 -1.0156e+00  1e+00  0e+00  3e+00\n",
      " 1:  8.3608e-03 -2.4456e-02  3e-02  7e-17  9e-02\n",
      " 2:  2.7342e-03 -1.0281e-03  4e-03  2e-16  4e-05\n",
      " 3:  1.5637e-03  1.3020e-03  3e-04  1e-16  9e-07\n",
      " 4:  1.4037e-03  1.3995e-03  4e-06  7e-17  9e-09\n",
      " 5:  1.4005e-03  1.4004e-03  4e-08  8e-17  9e-11\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  1.0662e-02 -1.0137e+00  1e+00  4e-16  3e+00\n",
      " 1:  9.9708e-03 -2.2393e-02  3e-02  1e-16  9e-02\n",
      " 2:  4.9300e-03  1.3649e-03  4e-03  1e-16  7e-04\n",
      " 3:  3.8715e-03  3.6147e-03  3e-04  6e-17  1e-05\n",
      " 4:  3.6961e-03  3.6886e-03  7e-06  8e-17  1e-07\n",
      " 5:  3.6894e-03  3.6894e-03  7e-08  2e-16  1e-09\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  1.2441e-02 -1.0115e+00  1e+00  2e-16  3e+00\n",
      " 1:  1.1774e-02 -2.0095e-02  3e-02  7e-17  9e-02\n",
      " 2:  7.2844e-03  3.9417e-03  3e-03  7e-17  1e-03\n",
      " 3:  6.3635e-03  6.1079e-03  3e-04  6e-17  2e-05\n",
      " 4:  6.1881e-03  6.1734e-03  1e-05  8e-17  8e-08\n",
      " 5:  6.1746e-03  6.1744e-03  2e-07  2e-16  8e-10\n",
      " 6:  6.1744e-03  6.1744e-03  2e-09  1e-16  8e-12\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  1.4434e-02 -1.0091e+00  1e+00  2e-16  3e+00\n",
      " 1:  1.3794e-02 -1.7539e-02  3e-02  8e-17  8e-02\n",
      " 2:  9.8219e-03  6.7202e-03  3e-03  7e-17  2e-03\n",
      " 3:  9.0568e-03  8.8055e-03  3e-04  1e-16  2e-05\n",
      " 4:  8.9126e-03  8.8839e-03  3e-05  2e-16  7e-18\n",
      " 5:  8.8895e-03  8.8885e-03  1e-06  1e-16  2e-17\n",
      " 6:  8.8885e-03  8.8885e-03  1e-08  2e-16  2e-17\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  1.6668e-02 -1.0064e+00  1e+00  0e+00  3e+00\n",
      " 1:  1.6055e-02 -1.4696e-02  3e-02  4e-17  8e-02\n",
      " 2:  1.2569e-02  9.7210e-03  3e-03  1e-16  2e-03\n",
      " 3:  1.1968e-02  1.1718e-02  2e-04  8e-17  3e-05\n",
      " 4:  1.1878e-02  1.1843e-02  3e-05  4e-17  1e-17\n",
      " 5:  1.1867e-02  1.1862e-02  5e-06  6e-17  1e-17\n",
      " 6:  1.1866e-02  1.1866e-02  5e-07  8e-17  8e-18\n",
      " 7:  1.1866e-02  1.1866e-02  9e-09  8e-17  1e-17\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  1.9171e-02 -1.0034e+00  1e+00  1e-16  3e+00\n",
      " 1:  1.8588e-02 -1.1537e-02  3e-02  8e-17  8e-02\n",
      " 2:  1.5554e-02  1.2967e-02  3e-03  6e-17  2e-03\n",
      " 3:  1.5106e-02  1.4881e-02  2e-04  1e-16  3e-05\n",
      " 4:  1.5065e-02  1.5044e-02  2e-05  8e-17  2e-17\n",
      " 5:  1.5064e-02  1.5064e-02  3e-07  3e-17  2e-17\n",
      " 6:  1.5064e-02  1.5064e-02  3e-09  6e-17  1e-17\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  2.1975e-02 -1.0000e+00  1e+00  0e+00  3e+00\n",
      " 1:  2.1423e-02 -8.0283e-03  3e-02  4e-17  8e-02\n",
      " 2:  1.8808e-02  1.6485e-02  2e-03  8e-17  2e-03\n",
      " 3:  1.8492e-02  1.8311e-02  2e-04  6e-17  3e-05\n",
      " 4:  1.8477e-02  1.8471e-02  6e-06  6e-17  2e-17\n",
      " 5:  1.8477e-02  1.8477e-02  6e-08  7e-17  1e-17\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  2.5118e-02 -9.9630e-01  1e+00  1e-16  3e+00\n",
      " 1:  2.4597e-02 -4.1348e-03  3e-02  1e-16  8e-02\n",
      " 2:  2.2367e-02  2.0306e-02  2e-03  8e-17  2e-03\n",
      " 3:  2.2155e-02  2.2025e-02  1e-04  2e-16  3e-05\n",
      " 4:  2.2150e-02  2.2148e-02  2e-06  2e-16  2e-07\n",
      " 5:  2.2150e-02  2.2150e-02  2e-08  4e-17  2e-09\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  2.8638e-02 -9.9215e-01  1e+00  2e-16  3e+00\n",
      " 1:  2.8150e-02  1.8359e-04  3e-02  4e-17  7e-02\n",
      " 2:  2.6270e-02  2.4464e-02  2e-03  6e-17  2e-03\n",
      " 3:  2.6134e-02  2.6049e-02  8e-05  1e-16  2e-05\n",
      " 4:  2.6133e-02  2.6132e-02  1e-06  2e-16  2e-07\n",
      " 5:  2.6133e-02  2.6133e-02  1e-08  1e-16  2e-09\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  3.2582e-02 -9.8753e-01  1e+00  0e+00  3e+00\n",
      " 1:  3.2128e-02  4.9706e-03  3e-02  1e-16  7e-02\n",
      " 2:  3.0560e-02  2.8999e-02  2e-03  2e-16  2e-03\n",
      " 3:  3.0477e-02  3.0426e-02  5e-05  1e-16  2e-05\n",
      " 4:  3.0477e-02  3.0476e-02  5e-07  6e-17  2e-07\n",
      " 5:  3.0477e-02  3.0477e-02  5e-09  6e-17  2e-09\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  3.7001e-02 -9.8240e-01  1e+00  3e-16  3e+00\n",
      " 1:  3.6581e-02  1.0274e-02  3e-02  4e-17  7e-02\n",
      " 2:  3.5290e-02  3.3958e-02  1e-03  7e-17  2e-03\n",
      " 3:  3.5241e-02  3.5210e-02  3e-05  1e-16  2e-05\n",
      " 4:  3.5241e-02  3.5240e-02  3e-07  1e-16  2e-07\n",
      " 5:  3.5241e-02  3.5241e-02  3e-09  2e-16  2e-09\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  4.1951e-02 -9.7670e-01  1e+00  2e-16  3e+00\n",
      " 1:  4.1566e-02  1.6148e-02  3e-02  1e-16  7e-02\n",
      " 2:  4.0515e-02  3.9395e-02  1e-03  3e-17  1e-03\n",
      " 3:  4.0487e-02  4.0469e-02  2e-05  2e-16  1e-05\n",
      " 4:  4.0487e-02  4.0487e-02  2e-07  1e-16  1e-07\n",
      " 5:  4.0487e-02  4.0487e-02  2e-09  8e-17  1e-09\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  4.7497e-02 -9.7036e-01  1e+00  2e-16  3e+00\n",
      " 1:  4.7146e-02  2.2651e-02  2e-02  1e-16  7e-02\n",
      " 2:  4.6301e-02  4.5370e-02  9e-04  1e-16  1e-03\n",
      " 3:  4.6287e-02  4.6274e-02  1e-05  6e-17  1e-05\n",
      " 4:  4.6287e-02  4.6286e-02  1e-07  9e-17  1e-07\n",
      " 5:  4.6287e-02  4.6287e-02  1e-09  7e-17  1e-09\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  5.3711e-02 -9.6332e-01  1e+00  3e-16  3e+00\n",
      " 1:  5.3394e-02  2.9849e-02  2e-02  2e-16  6e-02\n",
      " 2:  5.2723e-02  5.1957e-02  8e-04  1e-16  1e-03\n",
      " 3:  5.2715e-02  5.2706e-02  9e-06  1e-16  1e-05\n",
      " 4:  5.2715e-02  5.2715e-02  9e-08  1e-16  1e-07\n",
      " 5:  5.2715e-02  5.2715e-02  9e-10  9e-17  1e-09\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  6.0673e-02 -9.5549e-01  1e+00  2e-16  3e+00\n",
      " 1:  6.0388e-02  3.7815e-02  2e-02  4e-17  6e-02\n",
      " 2:  5.9862e-02  5.9237e-02  6e-04  6e-17  1e-03\n",
      " 3:  5.9858e-02  5.9852e-02  7e-06  2e-16  1e-05\n",
      " 4:  5.9858e-02  5.9858e-02  7e-08  2e-16  1e-07\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  6.8473e-02 -9.4680e-01  1e+00  3e-16  3e+00\n",
      " 1:  6.8220e-02  4.6632e-02  2e-02  7e-17  6e-02\n",
      " 2:  6.7813e-02  6.7304e-02  5e-04  9e-17  8e-04\n",
      " 3:  6.7811e-02  6.7806e-02  5e-06  4e-17  8e-06\n",
      " 4:  6.7811e-02  6.7811e-02  5e-08  1e-16  8e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  7.7214e-02 -9.3715e-01  1e+00  2e-16  3e+00\n",
      " 1:  7.6991e-02  5.6393e-02  2e-02  7e-17  6e-02\n",
      " 2:  7.6679e-02  7.6264e-02  4e-04  9e-17  7e-04\n",
      " 3:  7.6678e-02  7.6674e-02  4e-06  2e-16  8e-06\n",
      " 4:  7.6678e-02  7.6678e-02  4e-08  1e-16  8e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  8.7010e-02 -9.2642e-01  1e+00  2e-16  3e+00\n",
      " 1:  8.6815e-02  6.7203e-02  2e-02  1e-16  5e-02\n",
      " 2:  8.6579e-02  8.6237e-02  3e-04  1e-16  7e-04\n",
      " 3:  8.6578e-02  8.6575e-02  3e-06  1e-16  7e-06\n",
      " 4:  8.6578e-02  8.6578e-02  3e-08  7e-17  7e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  9.7988e-02 -9.1450e-01  1e+00  0e+00  3e+00\n",
      " 1:  9.7819e-02  7.9179e-02  2e-02  1e-16  5e-02\n",
      " 2:  9.7643e-02  9.7357e-02  3e-04  9e-17  6e-04\n",
      " 3:  9.7643e-02  9.7640e-02  3e-06  5e-17  6e-06\n",
      " 4:  9.7643e-02  9.7643e-02  3e-08  1e-16  6e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  1.1029e-01 -9.0125e-01  1e+00  0e+00  3e+00\n",
      " 1:  1.1015e-01  9.2456e-02  2e-02  7e-17  5e-02\n",
      " 2:  1.1002e-01  1.0977e-01  2e-04  1e-16  5e-04\n",
      " 3:  1.1002e-01  1.1002e-01  2e-06  6e-17  5e-06\n",
      " 4:  1.1002e-01  1.1002e-01  2e-08  6e-17  5e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  1.2409e-01 -8.8650e-01  1e+00  2e-16  3e+00\n",
      " 1:  1.2396e-01  1.0719e-01  2e-02  1e-16  4e-02\n",
      " 2:  1.2387e-01  1.2366e-01  2e-04  7e-17  5e-04\n",
      " 3:  1.2387e-01  1.2387e-01  2e-06  6e-17  5e-06\n",
      " 4:  1.2387e-01  1.2387e-01  2e-08  2e-16  5e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  1.3955e-01 -8.7009e-01  1e+00  0e+00  3e+00\n",
      " 1:  1.3945e-01  1.2354e-01  2e-02  6e-17  4e-02\n",
      " 2:  1.3938e-01  1.3919e-01  2e-04  9e-17  5e-04\n",
      " 3:  1.3938e-01  1.3937e-01  2e-06  4e-17  5e-06\n",
      " 4:  1.3938e-01  1.3938e-01  2e-08  1e-16  5e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  1.5689e-01 -8.5183e-01  1e+00  2e-16  3e+00\n",
      " 1:  1.5680e-01  1.4172e-01  2e-02  2e-16  4e-02\n",
      " 2:  1.5675e-01  1.5658e-01  2e-04  1e-16  4e-04\n",
      " 3:  1.5675e-01  1.5675e-01  2e-06  1e-16  4e-06\n",
      " 4:  1.5675e-01  1.5675e-01  2e-08  1e-16  4e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  1.7633e-01 -8.3147e-01  1e+00  0e+00  3e+00\n",
      " 1:  1.7625e-01  1.6194e-01  1e-02  7e-17  4e-02\n",
      " 2:  1.7622e-01  1.7607e-01  2e-04  7e-17  4e-04\n",
      " 3:  1.7622e-01  1.7622e-01  2e-06  7e-17  4e-06\n",
      " 4:  1.7622e-01  1.7622e-01  2e-08  6e-17  4e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  1.9813e-01 -8.0878e-01  1e+00  1e-16  3e+00\n",
      " 1:  1.9807e-01  1.8446e-01  1e-02  6e-17  4e-02\n",
      " 2:  1.9804e-01  1.9790e-01  1e-04  1e-16  4e-04\n",
      " 3:  1.9804e-01  1.9804e-01  1e-06  7e-17  4e-06\n",
      " 4:  1.9804e-01  1.9804e-01  1e-08  6e-17  4e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  2.2258e-01 -7.8351e-01  1e+00  0e+00  3e+00\n",
      " 1:  2.2252e-01  2.0947e-01  1e-02  9e-17  3e-02\n",
      " 2:  2.2251e-01  2.2237e-01  1e-04  2e-16  4e-04\n",
      " 3:  2.2251e-01  2.2251e-01  1e-06  2e-16  4e-06\n",
      " 4:  2.2251e-01  2.2251e-01  1e-08  5e-17  4e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  2.5000e-01 -7.5630e-01  1e+00  0e+00  3e+00\n",
      " 1:  2.4995e-01  2.3701e-01  1e-02  1e-16  3e-02\n",
      " 2:  2.4994e-01  2.4981e-01  1e-04  9e-17  4e-04\n",
      " 3:  2.4994e-01  2.4994e-01  1e-06  6e-17  4e-06\n",
      " 4:  2.4994e-01  2.4994e-01  1e-08  4e-17  4e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  2.8075e-01 -7.2573e-01  1e+00  0e+00  3e+00\n",
      " 1:  2.8071e-01  2.6791e-01  1e-02  7e-17  3e-02\n",
      " 2:  2.8070e-01  2.8057e-01  1e-04  5e-17  3e-04\n",
      " 3:  2.8070e-01  2.8070e-01  1e-06  1e-16  3e-06\n",
      " 4:  2.8070e-01  2.8070e-01  1e-08  1e-16  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  3.1525e-01 -6.9142e-01  1e+00  0e+00  3e+00\n",
      " 1:  3.1521e-01  3.0257e-01  1e-02  1e-16  3e-02\n",
      " 2:  3.1521e-01  3.1508e-01  1e-04  7e-17  3e-04\n",
      " 3:  3.1521e-01  3.1521e-01  1e-06  6e-17  3e-06\n",
      " 4:  3.1521e-01  3.1521e-01  1e-08  6e-17  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  3.5394e-01 -6.5289e-01  1e+00  1e-16  3e+00\n",
      " 1:  3.5392e-01  3.4143e-01  1e-02  2e-16  3e-02\n",
      " 2:  3.5391e-01  3.5379e-01  1e-04  2e-16  3e-04\n",
      " 3:  3.5391e-01  3.5391e-01  1e-06  1e-16  3e-06\n",
      " 4:  3.5391e-01  3.5391e-01  1e-08  7e-17  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  3.9735e-01 -6.0963e-01  1e+00  0e+00  3e+00\n",
      " 1:  3.9733e-01  3.8502e-01  1e-02  4e-17  3e-02\n",
      " 2:  3.9733e-01  3.9720e-01  1e-04  1e-16  3e-04\n",
      " 3:  3.9733e-01  3.9732e-01  1e-06  1e-16  3e-06\n",
      " 4:  3.9733e-01  3.9733e-01  1e-08  1e-16  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  4.4605e-01 -5.6108e-01  1e+00  0e+00  3e+00\n",
      " 1:  4.4603e-01  4.3390e-01  1e-02  9e-17  3e-02\n",
      " 2:  4.4603e-01  4.4590e-01  1e-04  3e-17  3e-04\n",
      " 3:  4.4603e-01  4.4603e-01  1e-06  8e-17  3e-06\n",
      " 4:  4.4603e-01  4.4603e-01  1e-08  1e-16  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  5.0068e-01 -5.0657e-01  1e+00  4e-16  3e+00\n",
      " 1:  5.0066e-01  4.8871e-01  1e-02  7e-17  3e-02\n",
      " 2:  5.0066e-01  5.0054e-01  1e-04  7e-17  3e-04\n",
      " 3:  5.0066e-01  5.0066e-01  1e-06  7e-17  3e-06\n",
      " 4:  5.0066e-01  5.0066e-01  1e-08  1e-16  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  5.6197e-01 -4.4540e-01  1e+00  2e-16  3e+00\n",
      " 1:  5.6196e-01  5.5018e-01  1e-02  3e-17  3e-02\n",
      " 2:  5.6195e-01  5.6184e-01  1e-04  1e-16  3e-04\n",
      " 3:  5.6195e-01  5.6195e-01  1e-06  7e-17  3e-06\n",
      " 4:  5.6195e-01  5.6195e-01  1e-08  7e-17  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  6.3073e-01 -3.7675e-01  1e+00  1e-16  3e+00\n",
      " 1:  6.3072e-01  6.1912e-01  1e-02  7e-17  3e-02\n",
      " 2:  6.3072e-01  6.3060e-01  1e-04  4e-17  3e-04\n",
      " 3:  6.3072e-01  6.3072e-01  1e-06  9e-17  3e-06\n",
      " 4:  6.3072e-01  6.3072e-01  1e-08  1e-16  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  7.0788e-01 -2.9970e-01  1e+00  0e+00  3e+00\n",
      " 1:  7.0787e-01  6.9644e-01  1e-02  1e-16  3e-02\n",
      " 2:  7.0787e-01  7.0776e-01  1e-04  8e-17  3e-04\n",
      " 3:  7.0787e-01  7.0787e-01  1e-06  2e-16  3e-06\n",
      " 4:  7.0787e-01  7.0787e-01  1e-08  1e-16  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  7.9444e-01 -2.1323e-01  1e+00  1e-16  3e+00\n",
      " 1:  7.9443e-01  7.8315e-01  1e-02  2e-16  3e-02\n",
      " 2:  7.9443e-01  7.9432e-01  1e-04  2e-16  3e-04\n",
      " 3:  7.9443e-01  7.9443e-01  1e-06  1e-16  3e-06\n",
      " 4:  7.9443e-01  7.9443e-01  1e-08  1e-16  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  8.9155e-01 -1.1620e-01  1e+00  0e+00  3e+00\n",
      " 1:  8.9154e-01  8.8041e-01  1e-02  5e-17  3e-02\n",
      " 2:  8.9154e-01  8.9143e-01  1e-04  7e-17  3e-04\n",
      " 3:  8.9154e-01  8.9154e-01  1e-06  7e-17  3e-06\n",
      " 4:  8.9154e-01  8.9154e-01  1e-08  8e-17  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  1.0005e+00 -7.3187e-03  1e+00  0e+00  3e+00\n",
      " 1:  1.0005e+00  9.8951e-01  1e-02  9e-17  3e-02\n",
      " 2:  1.0005e+00  1.0004e+00  1e-04  1e-16  3e-04\n",
      " 3:  1.0005e+00  1.0005e+00  1e-06  9e-17  3e-06\n",
      " 4:  1.0005e+00  1.0005e+00  1e-08  9e-17  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  1.1228e+00  1.1486e-01  1e+00  1e-16  3e+00\n",
      " 1:  1.1228e+00  1.1119e+00  1e-02  7e-17  3e-02\n",
      " 2:  1.1228e+00  1.1226e+00  1e-04  8e-17  3e-04\n",
      " 3:  1.1228e+00  1.1228e+00  1e-06  8e-17  3e-06\n",
      " 4:  1.1228e+00  1.1228e+00  1e-08  2e-16  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  1.2599e+00  2.5197e-01  1e+00  1e-16  3e+00\n",
      " 1:  1.2599e+00  1.2492e+00  1e-02  2e-16  3e-02\n",
      " 2:  1.2599e+00  1.2598e+00  1e-04  1e-16  3e-04\n",
      " 3:  1.2599e+00  1.2599e+00  1e-06  7e-17  3e-06\n",
      " 4:  1.2599e+00  1.2599e+00  1e-08  7e-17  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  1.4138e+00  4.0581e-01  1e+00  2e-16  3e+00\n",
      " 1:  1.4138e+00  1.4032e+00  1e-02  7e-17  3e-02\n",
      " 2:  1.4138e+00  1.4137e+00  1e-04  7e-17  3e-04\n",
      " 3:  1.4138e+00  1.4138e+00  1e-06  1e-16  3e-06\n",
      " 4:  1.4138e+00  1.4138e+00  1e-08  9e-17  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  1.5865e+00  5.7844e-01  1e+00  0e+00  3e+00\n",
      " 1:  1.5865e+00  1.5759e+00  1e-02  8e-17  3e-02\n",
      " 2:  1.5865e+00  1.5864e+00  1e-04  2e-16  3e-04\n",
      " 3:  1.5865e+00  1.5865e+00  1e-06  2e-16  3e-06\n",
      " 4:  1.5865e+00  1.5865e+00  1e-08  7e-17  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  1.7802e+00  7.7213e-01  1e+00  2e-16  3e+00\n",
      " 1:  1.7802e+00  1.7697e+00  1e-02  9e-17  3e-02\n",
      " 2:  1.7802e+00  1.7801e+00  1e-04  9e-17  3e-04\n",
      " 3:  1.7802e+00  1.7802e+00  1e-06  1e-16  3e-06\n",
      " 4:  1.7802e+00  1.7802e+00  1e-08  9e-17  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  1.9976e+00  9.8947e-01  1e+00  0e+00  3e+00\n",
      " 1:  1.9976e+00  1.9872e+00  1e-02  7e-17  3e-02\n",
      " 2:  1.9976e+00  1.9975e+00  1e-04  5e-17  3e-04\n",
      " 3:  1.9976e+00  1.9976e+00  1e-06  9e-17  3e-06\n",
      " 4:  1.9976e+00  1.9976e+00  1e-08  6e-17  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  2.2415e+00  1.2333e+00  1e+00  2e-16  3e+00\n",
      " 1:  2.2415e+00  2.2311e+00  1e-02  1e-16  3e-02\n",
      " 2:  2.2415e+00  2.2414e+00  1e-04  5e-17  3e-04\n",
      " 3:  2.2415e+00  2.2415e+00  1e-06  7e-17  3e-06\n",
      " 4:  2.2415e+00  2.2415e+00  1e-08  1e-16  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  2.5152e+00  1.5070e+00  1e+00  0e+00  3e+00\n",
      " 1:  2.5152e+00  2.5048e+00  1e-02  1e-16  3e-02\n",
      " 2:  2.5152e+00  2.5151e+00  1e-04  2e-16  3e-04\n",
      " 3:  2.5152e+00  2.5152e+00  1e-06  1e-16  3e-06\n",
      " 4:  2.5152e+00  2.5152e+00  1e-08  1e-16  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  2.8222e+00  1.8140e+00  1e+00  2e-16  3e+00\n",
      " 1:  2.8222e+00  2.8119e+00  1e-02  1e-16  3e-02\n",
      " 2:  2.8222e+00  2.8221e+00  1e-04  3e-17  3e-04\n",
      " 3:  2.8222e+00  2.8222e+00  1e-06  1e-16  3e-06\n",
      " 4:  2.8222e+00  2.8222e+00  1e-08  5e-17  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  3.1667e+00  2.1585e+00  1e+00  2e-16  3e+00\n",
      " 1:  3.1667e+00  3.1565e+00  1e-02  9e-17  3e-02\n",
      " 2:  3.1667e+00  3.1666e+00  1e-04  6e-17  3e-04\n",
      " 3:  3.1667e+00  3.1667e+00  1e-06  6e-17  3e-06\n",
      " 4:  3.1667e+00  3.1667e+00  1e-08  2e-16  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  3.5533e+00  2.5450e+00  1e+00  2e-16  3e+00\n",
      " 1:  3.5533e+00  3.5431e+00  1e-02  9e-17  3e-02\n",
      " 2:  3.5533e+00  3.5532e+00  1e-04  1e-16  3e-04\n",
      " 3:  3.5533e+00  3.5533e+00  1e-06  8e-17  3e-06\n",
      " 4:  3.5533e+00  3.5533e+00  1e-08  9e-17  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  3.9870e+00  2.9787e+00  1e+00  4e-16  3e+00\n",
      " 1:  3.9870e+00  3.9768e+00  1e-02  1e-16  3e-02\n",
      " 2:  3.9870e+00  3.9869e+00  1e-04  8e-17  3e-04\n",
      " 3:  3.9870e+00  3.9870e+00  1e-06  2e-16  3e-06\n",
      " 4:  3.9870e+00  3.9870e+00  1e-08  6e-17  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  4.4736e+00  3.4653e+00  1e+00  2e-16  3e+00\n",
      " 1:  4.4736e+00  4.4635e+00  1e-02  1e-16  3e-02\n",
      " 2:  4.4736e+00  4.4735e+00  1e-04  2e-16  3e-04\n",
      " 3:  4.4736e+00  4.4736e+00  1e-06  2e-16  3e-06\n",
      " 4:  4.4736e+00  4.4736e+00  1e-08  9e-17  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  5.0197e+00  4.0113e+00  1e+00  0e+00  3e+00\n",
      " 1:  5.0197e+00  5.0095e+00  1e-02  1e-16  3e-02\n",
      " 2:  5.0197e+00  5.0196e+00  1e-04  1e-16  3e-04\n",
      " 3:  5.0197e+00  5.0197e+00  1e-06  7e-17  3e-06\n",
      " 4:  5.0197e+00  5.0197e+00  1e-08  1e-16  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  5.6323e+00  4.6239e+00  1e+00  2e-16  3e+00\n",
      " 1:  5.6323e+00  5.6221e+00  1e-02  1e-16  3e-02\n",
      " 2:  5.6323e+00  5.6322e+00  1e-04  6e-17  3e-04\n",
      " 3:  5.6323e+00  5.6323e+00  1e-06  6e-17  3e-06\n",
      " 4:  5.6323e+00  5.6323e+00  1e-08  7e-17  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  6.3197e+00  5.3113e+00  1e+00  0e+00  3e+00\n",
      " 1:  6.3197e+00  6.3095e+00  1e-02  3e-17  3e-02\n",
      " 2:  6.3197e+00  6.3196e+00  1e-04  1e-16  3e-04\n",
      " 3:  6.3197e+00  6.3197e+00  1e-06  5e-17  3e-06\n",
      " 4:  6.3197e+00  6.3197e+00  1e-08  8e-17  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  7.0909e+00  6.0826e+00  1e+00  0e+00  3e+00\n",
      " 1:  7.0909e+00  7.0808e+00  1e-02  1e-16  3e-02\n",
      " 2:  7.0909e+00  7.0908e+00  1e-04  7e-17  3e-04\n",
      " 3:  7.0909e+00  7.0909e+00  1e-06  2e-16  3e-06\n",
      " 4:  7.0909e+00  7.0909e+00  1e-08  7e-17  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  7.9563e+00  6.9479e+00  1e+00  0e+00  3e+00\n",
      " 1:  7.9563e+00  7.9462e+00  1e-02  1e-16  3e-02\n",
      " 2:  7.9563e+00  7.9562e+00  1e-04  7e-17  3e-04\n",
      " 3:  7.9563e+00  7.9563e+00  1e-06  1e-16  3e-06\n",
      " 4:  7.9563e+00  7.9563e+00  1e-08  2e-16  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  8.9273e+00  7.9189e+00  1e+00  0e+00  3e+00\n",
      " 1:  8.9273e+00  8.9172e+00  1e-02  2e-16  3e-02\n",
      " 2:  8.9273e+00  8.9272e+00  1e-04  2e-16  3e-04\n",
      " 3:  8.9273e+00  8.9273e+00  1e-06  2e-16  3e-06\n",
      " 4:  8.9273e+00  8.9273e+00  1e-08  2e-16  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  1.0017e+01  9.0083e+00  1e+00  1e-16  3e+00\n",
      " 1:  1.0017e+01  1.0007e+01  1e-02  8e-17  3e-02\n",
      " 2:  1.0017e+01  1.0017e+01  1e-04  9e-17  3e-04\n",
      " 3:  1.0017e+01  1.0017e+01  1e-06  1e-16  3e-06\n",
      " 4:  1.0017e+01  1.0017e+01  1e-08  1e-16  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  1.1239e+01  1.0231e+01  1e+00  3e-16  3e+00\n",
      " 1:  1.1239e+01  1.1229e+01  1e-02  9e-17  3e-02\n",
      " 2:  1.1239e+01  1.1239e+01  1e-04  7e-17  3e-04\n",
      " 3:  1.1239e+01  1.1239e+01  1e-06  6e-17  3e-06\n",
      " 4:  1.1239e+01  1.1239e+01  1e-08  9e-17  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  1.2611e+01  1.1602e+01  1e+00  0e+00  3e+00\n",
      " 1:  1.2611e+01  1.2600e+01  1e-02  6e-17  3e-02\n",
      " 2:  1.2611e+01  1.2610e+01  1e-04  1e-16  3e-04\n",
      " 3:  1.2611e+01  1.2611e+01  1e-06  9e-17  3e-06\n",
      " 4:  1.2611e+01  1.2611e+01  1e-08  2e-16  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  1.4149e+01  1.3141e+01  1e+00  2e-16  3e+00\n",
      " 1:  1.4149e+01  1.4139e+01  1e-02  1e-16  3e-02\n",
      " 2:  1.4149e+01  1.4149e+01  1e-04  8e-17  3e-04\n",
      " 3:  1.4149e+01  1.4149e+01  1e-06  1e-16  3e-06\n",
      " 4:  1.4149e+01  1.4149e+01  1e-08  1e-16  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  1.5876e+01  1.4868e+01  1e+00  2e-16  3e+00\n",
      " 1:  1.5876e+01  1.5866e+01  1e-02  2e-16  3e-02\n",
      " 2:  1.5876e+01  1.5876e+01  1e-04  1e-16  3e-04\n",
      " 3:  1.5876e+01  1.5876e+01  1e-06  9e-17  3e-06\n",
      " 4:  1.5876e+01  1.5876e+01  1e-08  2e-16  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  1.7813e+01  1.6805e+01  1e+00  1e-16  3e+00\n",
      " 1:  1.7813e+01  1.7803e+01  1e-02  5e-17  3e-02\n",
      " 2:  1.7813e+01  1.7813e+01  1e-04  4e-17  3e-04\n",
      " 3:  1.7813e+01  1.7813e+01  1e-06  7e-17  3e-06\n",
      " 4:  1.7813e+01  1.7813e+01  1e-08  8e-17  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  1.9987e+01  1.8979e+01  1e+00  2e-16  3e+00\n",
      " 1:  1.9987e+01  1.9977e+01  1e-02  2e-16  3e-02\n",
      " 2:  1.9987e+01  1.9987e+01  1e-04  7e-17  3e-04\n",
      " 3:  1.9987e+01  1.9987e+01  1e-06  1e-16  3e-06\n",
      " 4:  1.9987e+01  1.9987e+01  1e-08  1e-16  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  2.2426e+01  2.1418e+01  1e+00  1e-16  3e+00\n",
      " 1:  2.2426e+01  2.2416e+01  1e-02  1e-16  3e-02\n",
      " 2:  2.2426e+01  2.2426e+01  1e-04  3e-17  3e-04\n",
      " 3:  2.2426e+01  2.2426e+01  1e-06  1e-16  3e-06\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " 4:  2.2426e+01  2.2426e+01  1e-08  1e-16  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  2.5163e+01  2.4154e+01  1e+00  2e-16  3e+00\n",
      " 1:  2.5163e+01  2.5152e+01  1e-02  9e-17  3e-02\n",
      " 2:  2.5163e+01  2.5162e+01  1e-04  1e-16  3e-04\n",
      " 3:  2.5163e+01  2.5163e+01  1e-06  2e-16  3e-06\n",
      " 4:  2.5163e+01  2.5163e+01  1e-08  1e-16  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  2.8233e+01  2.7225e+01  1e+00  0e+00  3e+00\n",
      " 1:  2.8233e+01  2.8223e+01  1e-02  6e-17  3e-02\n",
      " 2:  2.8233e+01  2.8233e+01  1e-04  9e-17  3e-04\n",
      " 3:  2.8233e+01  2.8233e+01  1e-06  3e-17  3e-06\n",
      " 4:  2.8233e+01  2.8233e+01  1e-08  9e-17  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  3.1678e+01  3.0670e+01  1e+00  2e-16  3e+00\n",
      " 1:  3.1678e+01  3.1668e+01  1e-02  6e-17  3e-02\n",
      " 2:  3.1678e+01  3.1678e+01  1e-04  1e-16  3e-04\n",
      " 3:  3.1678e+01  3.1678e+01  1e-06  4e-17  3e-06\n",
      " 4:  3.1678e+01  3.1678e+01  1e-08  1e-16  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  3.5544e+01  3.4535e+01  1e+00  0e+00  3e+00\n",
      " 1:  3.5544e+01  3.5533e+01  1e-02  9e-17  3e-02\n",
      " 2:  3.5544e+01  3.5543e+01  1e-04  8e-17  3e-04\n",
      " 3:  3.5544e+01  3.5544e+01  1e-06  1e-16  3e-06\n",
      " 4:  3.5544e+01  3.5544e+01  1e-08  9e-17  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  3.9881e+01  3.8872e+01  1e+00  2e-16  3e+00\n",
      " 1:  3.9881e+01  3.9871e+01  1e-02  5e-17  3e-02\n",
      " 2:  3.9881e+01  3.9881e+01  1e-04  2e-16  3e-04\n",
      " 3:  3.9881e+01  3.9881e+01  1e-06  2e-16  3e-06\n",
      " 4:  3.9881e+01  3.9881e+01  1e-08  8e-17  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  4.4747e+01  4.3739e+01  1e+00  0e+00  3e+00\n",
      " 1:  4.4747e+01  4.4737e+01  1e-02  4e-17  3e-02\n",
      " 2:  4.4747e+01  4.4747e+01  1e-04  1e-16  3e-04\n",
      " 3:  4.4747e+01  4.4747e+01  1e-06  1e-16  3e-06\n",
      " 4:  4.4747e+01  4.4747e+01  1e-08  2e-16  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  5.0207e+01  4.9199e+01  1e+00  2e-16  3e+00\n",
      " 1:  5.0207e+01  5.0197e+01  1e-02  7e-17  3e-02\n",
      " 2:  5.0207e+01  5.0207e+01  1e-04  5e-17  3e-04\n",
      " 3:  5.0207e+01  5.0207e+01  1e-06  7e-17  3e-06\n",
      " 4:  5.0207e+01  5.0207e+01  1e-08  7e-17  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  5.6333e+01  5.5325e+01  1e+00  0e+00  3e+00\n",
      " 1:  5.6333e+01  5.6323e+01  1e-02  7e-17  3e-02\n",
      " 2:  5.6333e+01  5.6333e+01  1e-04  1e-16  3e-04\n",
      " 3:  5.6333e+01  5.6333e+01  1e-06  2e-16  3e-06\n",
      " 4:  5.6333e+01  5.6333e+01  1e-08  1e-16  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  6.3207e+01  6.2199e+01  1e+00  3e-16  3e+00\n",
      " 1:  6.3207e+01  6.3197e+01  1e-02  5e-17  3e-02\n",
      " 2:  6.3207e+01  6.3207e+01  1e-04  7e-17  3e-04\n",
      " 3:  6.3207e+01  6.3207e+01  1e-06  1e-16  3e-06\n",
      " 4:  6.3207e+01  6.3207e+01  1e-08  8e-17  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  7.0920e+01  6.9911e+01  1e+00  0e+00  3e+00\n",
      " 1:  7.0920e+01  7.0910e+01  1e-02  1e-16  3e-02\n",
      " 2:  7.0920e+01  7.0920e+01  1e-04  6e-17  3e-04\n",
      " 3:  7.0920e+01  7.0920e+01  1e-06  5e-17  3e-06\n",
      " 4:  7.0920e+01  7.0920e+01  1e-08  1e-16  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  7.9574e+01  7.8565e+01  1e+00  2e-16  3e+00\n",
      " 1:  7.9574e+01  7.9563e+01  1e-02  7e-17  3e-02\n",
      " 2:  7.9574e+01  7.9573e+01  1e-04  6e-17  3e-04\n",
      " 3:  7.9574e+01  7.9574e+01  1e-06  1e-16  3e-06\n",
      " 4:  7.9574e+01  7.9574e+01  1e-08  2e-16  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  8.9283e+01  8.8275e+01  1e+00  0e+00  3e+00\n",
      " 1:  8.9283e+01  8.9273e+01  1e-02  1e-16  3e-02\n",
      " 2:  8.9283e+01  8.9283e+01  1e-04  7e-17  3e-04\n",
      " 3:  8.9283e+01  8.9283e+01  1e-06  9e-17  3e-06\n",
      " 4:  8.9283e+01  8.9283e+01  1e-08  1e-16  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  1.0018e+02  9.9169e+01  1e+00  1e-16  3e+00\n",
      " 1:  1.0018e+02  1.0017e+02  1e-02  8e-17  3e-02\n",
      " 2:  1.0018e+02  1.0018e+02  1e-04  8e-17  3e-04\n",
      " 3:  1.0018e+02  1.0018e+02  1e-06  2e-16  3e-06\n",
      " 4:  1.0018e+02  1.0018e+02  1e-08  1e-16  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  1.1240e+02  1.1139e+02  1e+00  4e-16  3e+00\n",
      " 1:  1.1240e+02  1.1239e+02  1e-02  1e-16  3e-02\n",
      " 2:  1.1240e+02  1.1240e+02  1e-04  1e-16  3e-04\n",
      " 3:  1.1240e+02  1.1240e+02  1e-06  7e-17  3e-06\n",
      " 4:  1.1240e+02  1.1240e+02  1e-08  4e-17  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  1.2612e+02  1.2511e+02  1e+00  2e-16  3e+00\n",
      " 1:  1.2612e+02  1.2611e+02  1e-02  6e-17  3e-02\n",
      " 2:  1.2612e+02  1.2612e+02  1e-04  8e-17  3e-04\n",
      " 3:  1.2612e+02  1.2612e+02  1e-06  1e-16  3e-06\n",
      " 4:  1.2612e+02  1.2612e+02  1e-08  6e-17  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  1.4150e+02  1.4050e+02  1e+00  0e+00  3e+00\n",
      " 1:  1.4150e+02  1.4149e+02  1e-02  1e-16  3e-02\n",
      " 2:  1.4150e+02  1.4150e+02  1e-04  7e-17  3e-04\n",
      " 3:  1.4150e+02  1.4150e+02  1e-06  6e-17  3e-06\n",
      " 4:  1.4150e+02  1.4150e+02  1e-08  1e-16  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  1.5877e+02  1.5776e+02  1e+00  1e-16  3e+00\n",
      " 1:  1.5877e+02  1.5876e+02  1e-02  5e-17  3e-02\n",
      " 2:  1.5877e+02  1.5877e+02  1e-04  7e-17  3e-04\n",
      " 3:  1.5877e+02  1.5877e+02  1e-06  9e-17  3e-06\n",
      " 4:  1.5877e+02  1.5877e+02  1e-08  4e-17  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  1.7814e+02  1.7714e+02  1e+00  0e+00  3e+00\n",
      " 1:  1.7814e+02  1.7813e+02  1e-02  6e-17  3e-02\n",
      " 2:  1.7814e+02  1.7814e+02  1e-04  1e-16  3e-04\n",
      " 3:  1.7814e+02  1.7814e+02  1e-06  9e-17  3e-06\n",
      " 4:  1.7814e+02  1.7814e+02  1e-08  1e-16  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  1.9988e+02  1.9887e+02  1e+00  2e-16  3e+00\n",
      " 1:  1.9988e+02  1.9987e+02  1e-02  9e-17  3e-02\n",
      " 2:  1.9988e+02  1.9988e+02  1e-04  7e-17  3e-04\n",
      " 3:  1.9988e+02  1.9988e+02  1e-06  7e-17  3e-06\n",
      " 4:  1.9988e+02  1.9988e+02  1e-08  1e-16  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  2.2427e+02  2.2326e+02  1e+00  0e+00  3e+00\n",
      " 1:  2.2427e+02  2.2426e+02  1e-02  7e-17  3e-02\n",
      " 2:  2.2427e+02  2.2427e+02  1e-04  5e-17  3e-04\n",
      " 3:  2.2427e+02  2.2427e+02  1e-06  1e-16  3e-06\n",
      " 4:  2.2427e+02  2.2427e+02  1e-08  9e-17  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  2.5164e+02  2.5063e+02  1e+00  1e-16  3e+00\n",
      " 1:  2.5164e+02  2.5163e+02  1e-02  6e-17  3e-02\n",
      " 2:  2.5164e+02  2.5164e+02  1e-04  1e-16  3e-04\n",
      " 3:  2.5164e+02  2.5164e+02  1e-06  9e-17  3e-06\n",
      " 4:  2.5164e+02  2.5164e+02  1e-08  7e-17  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  2.8234e+02  2.8133e+02  1e+00  4e-16  3e+00\n",
      " 1:  2.8234e+02  2.8233e+02  1e-02  6e-17  3e-02\n",
      " 2:  2.8234e+02  2.8234e+02  1e-04  6e-17  3e-04\n",
      " 3:  2.8234e+02  2.8234e+02  1e-06  1e-16  3e-06\n",
      " 4:  2.8234e+02  2.8234e+02  1e-08  1e-16  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  3.1679e+02  3.1578e+02  1e+00  2e-16  3e+00\n",
      " 1:  3.1679e+02  3.1678e+02  1e-02  9e-17  3e-02\n",
      " 2:  3.1679e+02  3.1679e+02  1e-04  9e-17  3e-04\n",
      " 3:  3.1679e+02  3.1679e+02  1e-06  1e-16  3e-06\n",
      " 4:  3.1679e+02  3.1679e+02  1e-08  6e-17  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  3.5545e+02  3.5444e+02  1e+00  2e-16  3e+00\n",
      " 1:  3.5545e+02  3.5544e+02  1e-02  1e-16  3e-02\n",
      " 2:  3.5545e+02  3.5545e+02  1e-04  4e-17  3e-04\n",
      " 3:  3.5545e+02  3.5545e+02  1e-06  1e-16  3e-06\n",
      " 4:  3.5545e+02  3.5545e+02  1e-08  6e-17  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  3.9882e+02  3.9781e+02  1e+00  0e+00  3e+00\n",
      " 1:  3.9882e+02  3.9881e+02  1e-02  6e-17  3e-02\n",
      " 2:  3.9882e+02  3.9882e+02  1e-04  7e-17  3e-04\n",
      " 3:  3.9882e+02  3.9882e+02  1e-06  9e-17  3e-06\n",
      " 4:  3.9882e+02  3.9882e+02  1e-08  9e-17  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  4.4748e+02  4.4647e+02  1e+00  2e-16  3e+00\n",
      " 1:  4.4748e+02  4.4747e+02  1e-02  4e-17  3e-02\n",
      " 2:  4.4748e+02  4.4748e+02  1e-04  7e-17  3e-04\n",
      " 3:  4.4748e+02  4.4748e+02  1e-06  1e-16  3e-06\n",
      " 4:  4.4748e+02  4.4748e+02  1e-08  1e-16  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  5.0208e+02  5.0107e+02  1e+00  2e-16  3e+00\n",
      " 1:  5.0208e+02  5.0207e+02  1e-02  6e-17  3e-02\n",
      " 2:  5.0208e+02  5.0208e+02  1e-04  1e-16  3e-04\n",
      " 3:  5.0208e+02  5.0208e+02  1e-06  6e-17  3e-06\n",
      " 4:  5.0208e+02  5.0208e+02  1e-08  1e-16  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  5.6334e+02  5.6234e+02  1e+00  0e+00  3e+00\n",
      " 1:  5.6334e+02  5.6333e+02  1e-02  2e-16  3e-02\n",
      " 2:  5.6334e+02  5.6334e+02  1e-04  2e-16  3e-04\n",
      " 3:  5.6334e+02  5.6334e+02  1e-06  1e-16  3e-06\n",
      " 4:  5.6334e+02  5.6334e+02  1e-08  6e-17  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  6.3208e+02  6.3107e+02  1e+00  1e-16  3e+00\n",
      " 1:  6.3208e+02  6.3207e+02  1e-02  1e-16  3e-02\n",
      " 2:  6.3208e+02  6.3208e+02  1e-04  6e-17  3e-04\n",
      " 3:  6.3208e+02  6.3208e+02  1e-06  1e-16  3e-06\n",
      " 4:  6.3208e+02  6.3208e+02  1e-08  9e-17  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  7.0921e+02  7.0820e+02  1e+00  1e-16  3e+00\n",
      " 1:  7.0921e+02  7.0920e+02  1e-02  2e-16  3e-02\n",
      " 2:  7.0921e+02  7.0921e+02  1e-04  2e-16  3e-04\n",
      " 3:  7.0921e+02  7.0921e+02  1e-06  7e-17  3e-06\n",
      " 4:  7.0921e+02  7.0921e+02  1e-08  7e-17  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  7.9575e+02  7.9474e+02  1e+00  0e+00  3e+00\n",
      " 1:  7.9575e+02  7.9574e+02  1e-02  7e-17  3e-02\n",
      " 2:  7.9575e+02  7.9575e+02  1e-04  6e-17  3e-04\n",
      " 3:  7.9575e+02  7.9575e+02  1e-06  7e-17  3e-06\n",
      " 4:  7.9575e+02  7.9575e+02  1e-08  2e-16  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  8.9284e+02  8.9183e+02  1e+00  1e-16  3e+00\n",
      " 1:  8.9284e+02  8.9283e+02  1e-02  2e-16  3e-02\n",
      " 2:  8.9284e+02  8.9284e+02  1e-04  7e-17  3e-04\n",
      " 3:  8.9284e+02  8.9284e+02  1e-06  6e-17  3e-06\n",
      " 4:  8.9284e+02  8.9284e+02  1e-08  6e-17  3e-08\n",
      "Optimal solution found.\n",
      "     pcost       dcost       gap    pres   dres\n",
      " 0: -4.2046e-04 -1.0275e+00  1e+00  0e+00  3e+00\n",
      " 1: -1.2945e-03 -3.7097e-02  4e-02  7e-17  1e-01\n",
      " 2: -1.4526e-02 -2.2771e-02  8e-03  1e-16  2e-17\n",
      " 3: -1.6678e-02 -1.7397e-02  7e-04  1e-16  1e-17\n",
      " 4: -1.7128e-02 -1.7169e-02  4e-05  1e-16  2e-17\n",
      " 5: -1.7164e-02 -1.7164e-02  9e-07  1e-18  1e-17\n",
      " 6: -1.7164e-02 -1.7164e-02  9e-09  6e-17  3e-17\n",
      "Optimal solution found.\n"
     ]
    }
   ],
   "source": [
    "weights, returns, risks = optimize(return_vec)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "100"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(returns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "config": {
        "plotlyServerURL": "https://plot.ly"
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       "                            \n",
       "var gd = document.getElementById('2f0858a3-9da7-4742-b710-f5cc3186b128');\n",
       "var x = new MutationObserver(function (mutations, observer) {{\n",
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = go.Figure()\n",
    "fig.update_layout(xaxis_title='Standard Deviation', \n",
    "                  yaxis_title='Mean',\n",
    "                  showlegend=False)\n",
    "fig.add_trace(go.Scatter(x=stds.flatten(), y=means.flatten(),mode='markers'))\n",
    "fig.add_trace(go.Scatter(x=risks,y=returns,mode='markers+lines',name='Efficient Frontier'))\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[7.41881179e-01],\n",
       "       [2.27846533e-06],\n",
       "       [2.58116492e-01],\n",
       "       [4.60261471e-08],\n",
       "       [4.30464084e-09]])"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weights"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [],
   "source": [
    "sum_weights=0\n",
    "for each in weights:\n",
    "    sum_weights+=each[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum_weights"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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