This code accompanies the paper: E. van den Berg, "A hybrid quasi-Newton projected-gradient method with application to Lasso and basis-pursuit denoising," Math. Prog. Comp. 12, 1–38 (2020); see the arXiv preprint or the published journal paper.
The Matlab scripts depend on several MEX files for speed. The source code for the extensions are located in the private directory and can be compiled using the compile_projector_mex.m and compile_product_B_mex.m scripts (this may require installation/configuation of supported compilers for Matlab).
Some of the scripts may require installation of SPGL1 and the SPARCO test problem set for sparse reconstruction.
The hybrid solver builds on SPGL1. Incremental versions of the solver were developed and used at different stages of the project. The latest version of the solver can be found in solver_v05.m. An earlier version solver_v04.m is also provided to generate results some of the figures and tables.
There are several scripts that reproduce tables and figures from the paper. When available, these scripts use precomputed results that are stored in the cache directory. In order to regenerate the results, delete the appropriate files in the cache directory. The following table summarizes the relevant scripts and the associated tables and figures
| Script | generates |
|---|---|
plot_Pareto.m |
Figure 1 |
plot_mutual_coherence.m |
Figure 5a |
plot_Lipschitz.m |
Figures 5a-c |
plot_problem_duality.m |
Figures 7a,b |
plot_duality_gap.m |
Figure 7c,d |
table_sparse_x0.m |
Table 1 |
table_correlated.m |
Tables 2 and 3 |
table_sparco.m |
Tables 4, 5, and 6 |