PGA-based Predictor-Corrector Algorithms for Monotone Generalized Variational Inequality

TL;DR

This paper introduces PGA-based predictor-corrector algorithms for solving monotone generalized variational inequalities with Lipschitz continuous operators, emphasizing their parallelizability and effectiveness in sparsity recovery tasks.

Contribution

The paper proposes a novel class of PGA-based predictor-corrector algorithms tailored for MGVI, extending extragradient and projection contraction methods to a broader class of problems.

Findings

Algorithms demonstrate wide applicability in sparsity recovery.

Methods are well-suited for parallel computation in multi-block convex optimization.

Numerical simulations confirm the effectiveness of the proposed algorithms.

Abstract

In this paper, we consider the monotone generalized variational inequality (MGVI) where the monotone operator is Lipschitz continuous. Inspired by the extragradient method and the projection contraction algorithms for monotone variational inequality (MVI), we propose a class of PGA-based Predictor-Corrector algorithms for MGVI. A significant characteristic of our algorithms for separable multi-blocks convex optimization problems is that they can be well adapted for parallel computation. Numerical simulations about different models for sparsity recovery show the wide applicability and effectiveness of our proposed methods.