A Proximal Gradient Method with an Explicit Linesearch for Multiobjective Optimization

This repository contains the source codes for the numerical experiments described in the article:

Y. Bello-Cruz, J.G. Melo, L.F. Prudente, and R.V.G. Serra,
A Proximal Gradient Method with an Explicit Linesearch for Multiobjective Optimization, technical report, 2024.

Date: November 2024

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Contents

The repository includes the following routines:

Main Routine

• main.m
  Controls the execution of the experiments, allowing users to:
  • Select the problem to be solved.
  • Choose the optimization algorithm to apply.

Algorithms

• ProxGrad.m
  Contains implementations of:

  • Explicit-MPG: Explicit Multiobjective Proximal Gradient algorithm.
  • Armijo-MPG: Multiobjective Proximal Gradient with Armijo line search.
  • Implicit-MPG: Implicit Multiobjective Proximal Gradient algorithm.

• ProxGradAcc.m
  Contains implementations of:

  • Accelerated-MPG: Accelerated Multiobjective Proximal Gradient algorithm.
  • Normal-MPG: Normal Proximal Gradient algorithm.

Auxiliary Routines

• inip.m
  Defines the initial parameters for the optimization problems.

• evalg.m
  Implements the functions G_j.

• evalgradg.m
  Computes the gradient of the functions G_j.

• evalh.m
  Implements the functions H_j.

• datas.m
  Generates the data for the functions H_j.

• subproblemProxGrad.m
  Solves the subproblem required in the proximal gradient methods.

Line Search Routines

• explicitLS.m
  Implements the explicit line search used in Explicit-MPG.

• explicitLSone.m
  Handles the line search for a single objective function in Explicit-MPG.

• armijo.m
  Implements the Armijo line search used in Armijo-MPG.

• implicitLS.m
  Implements the implicit line search used in Implicit-MPG.

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Instructions

To run the numerical experiments:

1. Open the file main.m.
2. Select the desired problem and algorithm in the code.
3. Run the script and view the results on the screen.

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License

This project is licensed under the GNU General Public License (GPL) version 3. For more information, see the LICENSE file.