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Block cubic Newton with greedy selection

This repository contains the files related to the experiments reported in

A. Cristofari. Block cubic Newton with greedy selection. arXiv:2407.18150.

In the above paper, a second-order block coordinate descent method is proposed, named Inexact Block Cubic Newton (IBCN) method, using a greedy rule for the block selection and cubic models for the block update.

Author

Andrea Cristofari (e-mail: [email protected])

Licensing

IBCN is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. IBCN is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with IBCN. If not, see http://www.gnu.org/licenses/.

Usage

All codes are in Matlab. Two classes of unconstrained problems are considered, as described in the above paper.

  1. For sparse least squares (non-convex problems), just run the file main_sp_ls.m.

  2. For l2-regularized logistic regression (convex problems), first download the datasets gisette, leu and madelon from https://www.csie.ntu.edu.tw/~cjlin/libsvmtools/datasets/, then convert the files into matlab files and save them as gisette.mat, leu.mat and madelon.mat, respectively. In each matlab file, the instance matrix must be a sparse matrix named A and the label vector must be a vector named b. Then, run the file main_l2_log_reg.m.