Quasi Strongly $E$-preinvexity and its Relationships with Nonlinear Programming

TL;DR

This paper introduces new classes of strongly E-preinvex and E-invex functions, explores their properties and relationships, and applies these concepts to nonlinear programming to establish conditions for global optimality.

Contribution

It extends existing function classes to quasi and pseudo variants, providing new theoretical insights and demonstrating their application in nonlinear optimization.

Findings

Defined quasi strongly E-preinvex and related functions with examples

Established properties and relationships among these functions

Applied results to nonlinear programming to identify global minima

Abstract

In this paper, we extend the class of strongly $E$-preinvex and strongly $E$-invex functions to quasi strongly $E$-preinvex, quasi strongly $E$-invex and pseudo strongly $E$-invex functions. Some nontrivial suitable examples have been constructed in support of our definitions. Several interesting properties and relationships of these functions are discussed. Furthermore, to show the application of our results, we consider a nonlinear programming problem and show that the local minimum point is also a strictly global minimum.