A new regularization of equilibrium problems on Hadamard manifolds: applications to theories of desires

Abstract

In this paper, we introduce a new proximal algorithm for equilibrium problems on a genuine Hadamard manifold, using a new regularization term. We first extend recent existence results by considering pseudomonotone bifunctions and a weaker sufficient condition than the coer-civity assumption. Then, we consider the convergence of this proximal-like algorithm which can be applied to genuinely Hadamard manifolds and not only to specific ones, as in the recent literature. A striking point is that our new regularization term have a clear interpretation in a recent "variational rationality" approach of human behavior. It represents the resistance to change aspects of such human dynamics driven by motivation to change aspects. This allows us to give an application to the theories of desires, showing how an agent must escape to a succession of temporary traps to be able to reach, at the end, his desires.

Pareto solutions as limits of collective traps: an inexact multiobjective proximal point algorithm

“…It is worth mentioning that the present paper and Bento et al (2021) provide two variants of such Lewin's model when resistance to move is weak, with two different formulations of resistance to move. Then, both papers give an application to the theories of collective desires, showing how a group must escape to a succession of temporary traps to be able to reach, at the end, his desires.…”