A partial order principle and vector variational principle for $\epsilon$-efficient solutions in the sense of N\'{e}meth

TL;DR

This paper introduces a new partial order principle to derive a vector Ekeland variational principle for epsilon-efficient solutions, removing previous boundedness assumptions and generalizing existing results.

Contribution

It presents a novel partial order principle and extends Gerstewitz's functions to establish a more general vector EVP for epsilon-efficient solutions.

Findings

Removed the boundedness assumption for the objective function range.

Derived several generalized vector EVPs.

Improved existing results in vector variational analysis.

Abstract

In this paper, we establish a partial order principle, which is useful to deriving vector Ekeland variational principle (denoted by EVP). By using the partial order principle and extending Gerstewitz's functions, we obtain a vector EVP for $\epsilon$-efficient solutions in the sense of N\'{e}meth, which essentially improves the earlier results by removing a usual assumption for boundedness of range of the objective function. From this, we also deduce several special vector EVPs, which improve and generalize the related known results.