Nonlinear Versions of a Vector Maximal Principle

TL;DR

This paper develops nonlinear extensions of a vector maximality principle using advanced ordering principles, broadening the theoretical framework for vector optimization.

Contribution

It introduces nonlinear versions of a known vector maximality principle based on the Brezis-Browder ordering principle and its pseudometric variant.

Findings

Extended the vector maximality principle to nonlinear contexts

Utilized the Brezis-Browder ordering principle and its pseudometric version

Provided new theoretical tools for vector optimization

Abstract

Some nonlinear extensions of the vector maximality statement established by Goepfert, Tammer and Zalinescu [Nonl. Anal., 39 (2000), 909-922] are given. Basic instruments for these are the Brezis-Browder ordering principle [Advances Math., 21 (1976), 355-364] and a (pseudometric) version of it obtained in Turinici [Demonstr. Math., 22 (1989), 213-228].