The self regulation problem as an inexact steepest descent method for multicriteria optimization

TL;DR

This paper introduces an inexact steepest descent method with Armijo's rule for multicriteria optimization, proving convergence to Pareto points under quasi-convexity, and applies it to a psychological self-regulation model.

Contribution

It develops a novel inexact steepest descent algorithm with convergence guarantees for multicriteria optimization and applies it to psychological self-regulation modeling.

Findings

Guaranteed convergence to Pareto critical points under quasi-convexity

Method is well-defined and applicable to real-world problems

Provides a new link between optimization algorithms and psychological models

Abstract

In this paper, we study an inexact steepest descent method, with Armijo's rule, for multicriteria optimization. The sequence generated by the method is guaranteed to be well-defined. Assuming quasi-convexity of the multicriteria function we prove full convergence of the sequence to a critical Pareto point. As an application, this paper offers a model of self regulation in Psychology, using a recent variational rationality approach.