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How to Reach his Desires: Variational Rationality and the Equilibrium Problem on Hadamard Manifolds

Glaydston Bento(glaydston***at***ufg.br)
Joćo Cruz Neto(jxavier***at***ufpi.edu.br)
Pedro Soares(pedrosoares***at***uespi.br)
Antoine Soubeyran(antoine.soubeyran***at***gmail.com)

Abstract: In this paper we present a sufficient condition for the existence of a solution for an \mbox{equilibrium} problem on an Hadamard manifold and under suitable assumptions on the sectional curvature, we \mbox{propose} a framework for the convergence analysis of a proximal point algorithm to solve this equilibrium \mbox{problem}. Finally, we offer an application to the necessity for an agent to escape to a succession of temporary traps to be able to reach, at the end, his desires, using a recent ``variational rationality" approach of human behavior.

Keywords: Proximal algorithms, Equilibrium problem, Hadamard manifold, Desires, Trap, Worthwhile changes.

Category 1: Convex and Nonsmooth Optimization (Generalized Convexity/Monoticity )


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Entry Submitted: 08/15/2015
Entry Accepted: 08/15/2015
Entry Last Modified: 08/15/2015

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