Proximal algorithms with Bregman distances for bilevel equilibrium problems with application to the problem of "how routines form and change" in Economics and Management Sciences

TL;DR

This paper develops a proximal point algorithm using Bregman distances on Hadamard manifolds to solve bilevel equilibrium problems under pseudomonotonicity, with applications to organizational routines in Economics.

Contribution

It introduces a novel framework combining Bregman distances and Hadamard manifolds for bilevel equilibrium problems, extending convergence analysis under pseudomonotonicity.

Findings

Proposed a convergence framework for the algorithm.

Applied the method to organizational routines dynamics.

Validated the approach in economic modeling contexts.

Abstract

In this paper we present the bilevel equilibrium problem under conditions of pseudomonotonicity. Using Bregman distances on Hadamard manifolds we propose a framework for to analyse the convergence of a proximal point algorithm to solve this bilevel equilibrium problem. As an application, we consider the problem of "how routines form and change" which is crucial for the dynamics of organizations in Economics and Management Sciences.