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asga's Introduction

ASGA package

This matlab package provides a generic solver for Accelerated SubGradient Algorithm (ASGA) for solving structured nonsmooth convex problems of the form

min_x f(x)+g(x), x in C

for proper, convex, and lower semicontinuous f and g, and C is a simple constraint.

We provide a solver for solving the above-mentioned problem:

  • ASGA1: single-subproble Accelerated SubGradient Algorithm;
  • ASGA2: parameter-free single-subproble Accelerated SubGradient Algorithm;
  • ASGA3: double-subprobleAccelerated SubGradient Algorithm;
  • ASGA4: parameter-free double-subprobleAccelerated SubGradient Algorithm.

Using the package

Installation

All the functions in the package are given in the folder /MatlabCodes.

In order to use the function we recommend to execute the following command

addpath(genpath('.'))

if you are not working in the root folder of the package or replacing '.' by the location of the folder on your machine.

Examples:

We recommend to look at the following files to see how to use the package:

  • Demos/Demo_sparse_optimization.m: sparse recovery.

References

[1] M. Ahookhosh, Accelerated first-order methods for large-scale convexoptimization: nearly optimal complexity under strongconvexity, Mathematical Methods of Operations Research, 89, 319--353 (2019).

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