Exponentially E-preinvex and E-invex functions in mathematical programming

TL;DR

This paper introduces the concept of exponentially E-invex functions in the context of E-differentiable vector optimization, establishing properties and optimality conditions to advance generalized convexity theory.

Contribution

It defines exponentially E-invexity, explores its properties, and derives optimality conditions, providing a new framework for generalized convexity in vector optimization.

Findings

Properties of exponentially E-invex functions are established.

Sufficient optimality conditions are derived under generalized hypotheses.

An example illustrates the application of the new concept.

Abstract

In this paper, we introduce a new concept of generalized convexity for E-differentiable vector optimization problems. Namely, the notion of exponentially E-invexity is defined. Further, some properties and results of exponentially E-invex functions are studied. The sufficient optimality conditions are derived under appropriate (generalized) exponentially E-invexity hypotheses. To exemplify the application of our proposed concept, we have included an appropriate example.