A pre-order principle and set-valued Ekeland variational principle

TL;DR

This paper introduces a general set-valued Ekeland variational principle derived from a new pre-order principle, encompassing many existing principles and offering new results in the context of set-valued optimization.

Contribution

It establishes a novel pre-order principle and derives a comprehensive set-valued Ekeland variational principle that generalizes and improves upon existing results.

Findings

Unified framework for set-valued Ekeland variational principles

Includes many known principles as special cases

Provides new variants and improvements

Abstract

We establish a pre-order principle. From the principle, we obtain a very general set-valued Ekeland variational principle, where the objective function is a set-valued map taking values in a quasi ordered linear space and the perturbation contains a family of set-valued maps satisfying certain property. From this general set-valued Ekeland variational principle, we deduce a number of particular versions of set-valued Ekeland variational principle, which include many known Ekeland variational principles, their improvements and some new results.