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: andrea.cristofari@uniroma2.it)

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/. Using the libsvmread software, which can be downloaded from therein as well, 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.