Vector Optimization with Domination Structures: Variational Principles and Applications

TL;DR

This paper develops new variational principles for vector optimization problems in infinite-dimensional spaces, extending Ekeland's principle to domination structures, with applications in behavioral sciences.

Contribution

It introduces a novel extension of variational principles to domination vector settings, combining primal and dual methods for infinite-dimensional optimization.

Findings

New variational principles for domination vector problems.

Sufficient conditions for variational traps in behavioral models.

Extensions of Ekeland's principle to infinite-dimensional spaces.

Abstract

This paper addresses a large class of vector optimization problems in infinite-dimensional spaces with respect to two important binary relations derived from domination structures. Motivated by theoretical challenges as well as by applications to some models in behavioral sciences, we establish new variational principles that can be viewed as far-going extensions of the Ekeland variational principle to cover domination vector settings. Our approach combines advantages of both primal and dual techniques in variational analysis with providing useful suficient conditions for the existence of variational traps in behavioral science models with variable domination structures.