w-Invexity and Optimality Problem

TL;DR

This paper introduces a generalized class of functions called w-invex and related types, analyzing their properties and applying them to optimization problems to extend the theory of preinvex functions.

Contribution

It defines new classes of w-invex functions and explores their properties, providing a foundation for analyzing optimization problems with these functions.

Findings

Introduction of w-invex, w-preinvex, and related functions

Analysis of core properties of these functions

Application to optimization problem analysis

Abstract

We define w-invex set, w-preinvex, w-strictly preinvex, w-quasi preinvex, w-strictly quasi preinvex, w-semi-strictly quasi preinvex, and w-pre pseudo-invex functions in this context. And these form a class of real functions, which is the generalization of a family of preinvex functions. Here, we provide a thorough analysis of the core characteristics of these functions, along with numerous examples that help to illustrate the idea. Finally, w-quasi preinvex, w-strictly preinvex, and w-strictly quasi preinvex functions are used to analyze the optimization problems.