Non-linear programming problem for semi strongly $E$-preinvexity

TL;DR

This paper introduces semi strongly E-preinvexity and E-invexity, providing examples, exploring their properties on strongly E-invex sets, and analyzing a non-linear programming problem related to these functions.

Contribution

It defines new classes of functions, explores their properties, and studies their role in non-linear programming problems, expanding the theoretical framework.

Findings

Examples demonstrating semi strongly E-preinvexity and E-invexity.

Characterizations of these functions on strongly E-invex sets.

Relationships between optimal solutions and these functions.

Abstract

In this article, we present semi strongly $E$-preinvexity and semi strongly $E$-invexity. To demonstrate the existence of these functions, certain nontrivial examples have been developed. Several significant relationships and characterizations of these functions on strongly $E$-invex sets are discussed. Furthermore, we consider a non-linear programming problem for semi strongly $E$-preinvex functions and investigate relationships between the set of optimal solutions and these functions.