A proximal point algorithm with generalized proximal distances to BEPs

TL;DR

This paper introduces a proximal point algorithm with generalized proximal distances to solve bilevel equilibrium problems, providing a convergence framework applicable to various optimization and equilibrium scenarios.

Contribution

It presents a novel proximal point method with generalized distances for bilevel equilibrium problems and offers a convergence analysis framework for these algorithms.

Findings

Algorithm successfully solves bilevel equilibrium problems.

Framework ensures convergence of the generated sequences.

Applicable to mathematical programming and equilibrium constraint problems.

Abstract

We consider a bilevel problem involving two monotone equilibrium bifunctions and we show that this problem can be solved by a proximal point method with generalized proximal distances. We propose a framework for the convergence analysis of the sequences generated by the algorithm. This class of problems is very interesting because it covers mathematical programs and optimization problems under equilibrium constraints. As an application, we consider the problem of the stability and change dynamics of task's allocation in a hierarchical organization.