June 24, 2015

This subdirectory contains the following MATLAB source codes and folders:

Lp.m                main code of the penalty method

Lp_penalty.m        nonmonotone proximal gradient algorithm for solving unconstrained penalty subproblems

Lp2.m               main code of the penalty method for the regularized least squares model

Lp_penalty2.m       nonmonotone proximal gradient algorithm for solving unconstrained penalty subproblems for the regularized least squares model

Lp_proj.m           subroutine for computing the proximal operator for ||x||_p^p; last modified on March 6, 2017

explicitMatrix.m    Construct function handle for matrix multiplication

run_code2.m
run_code3.m
run_code53.m        Run code.

The runcodes require the package SPGL1, downloadable at http://www.cs.ubc.ca/~mpf/spgl1/download.html, for comparison

Implementation and numerical experience with the above codes are described in Section 5 of the paper: 
    Xiaojun Chen, Zhaosong Lu and Ting Kei Pong
    "Penalty Methods for Constrained Non-Lipschitz Optimization",
    Submitted.
This code was last updated on March 6, 2017.

Questions/comments/suggestions about the codes are welcome.  



Xiaojun Chen, maxjchen@polyu.edu.hk

Zhaosong Lu, zhaosong@sfu.ca

Ting Kei Pong, tk.pong@polyu.edu.hk