English

Strong Convergence of Relaxed Inertial Inexact Progressive Hedging Algorithm for Multi-stage Stochastic Variational Inequality Problems

Optimization and Control 2024-12-10 v1

Abstract

A Halpern-type relaxed inertial inexact progressive hedging algorithm (PHA) is proposed for solving multi-stage stochastic variational inequalities in general probability spaces. The subproblems in this algorithm are allowed to be calculated inexactly. It is found that the Halpern-type relaxed inertial inexact PHA is closely related to the Halpern-type relaxed inertial inexact proximal point algorithm (PPA). The strong convergence of the Halpern-type relaxed inertial inexact PHA is proved under appropriate conditions. Some numerical examples are given to indicate that the over-relaxed parameter and the inertial term can accelerate the convergence of the algorithm.

Cite

@article{arxiv.2412.05928,
  title  = {Strong Convergence of Relaxed Inertial Inexact Progressive Hedging Algorithm for Multi-stage Stochastic Variational Inequality Problems},
  author = {Jiaxin Chen and Zunjie Huang and Haisen Zhang},
  journal= {arXiv preprint arXiv:2412.05928},
  year   = {2024}
}