Refine Optimization Parameters

[devin-ai-integration]

Summary:

• Fixed import paths in test files to ensure correct module locations.
• Implemented a numerically stable sigmoid function to resolve overflow warnings.
• Enhanced logging for line search warnings in math_solvers.py to aid in diagnosing persistent issues.
• Adjusted optimization parameters in math_solvers.py to improve convergence and reduce warnings related to line search and gradient evaluations. This includes increasing the maximum number of iterations and adding alternative optimization methods.
• Refined test logic for time series analysis warnings in test_advanced_time_series_analysis.py to better handle and document warnings related to ARIMA and SARIMA models.
• Updated documentation to reflect all changes made and the reasoning behind them.
• Refined optimization parameters in test_numerical_optimization to resolve warnings. Removed the options parameter and adjusted the initial guess and method to 'Nelder-Mead'.

Checklist:

• All tests pass without warnings.
• Code changes have been documented.

Link to Devin run: https://preview.devin.ai/devin/e167658f782a40bb8a55abe144917961

This PR was written by Devin 👼

This Devin run was requested by kasinadhsarma.

If you have any feedback, you can leave comments in the PR and I'll address them in the app!