KKT conditions for optimization with generalized invex fuzzy functions

TL;DR

This paper extends the KKT optimality conditions to optimization problems involving nonsmooth, vector-valued, fuzzy functions with generalized invexity, broadening the scope of classical optimality frameworks.

Contribution

It introduces new KKT-type conditions for fuzzy optimization problems under weaker assumptions like invexity, without requiring differentiability or convexity.

Findings

Derived generalized KKT conditions for fuzzy functions

Unified and extended previous optimality results

Provided illustrative examples demonstrating applicability

Abstract

This paper explores optimality conditions in optimization problems involving generalized invex fuzzy functions. We extend the classical KKT framework to settings in which the objective and constraint functions are nonsmooth, vector-valued, and fuzzy-valued, and satisfy various generalized invexity conditions such as V-invexity, V-pseudoinvexity, and Vquasiinvexity. After reviewing key concepts from nonsmooth analysis and multiobjective optimization, we derive new KKT-type conditions under weaker assumptions than classical convexity, ensuring (weak) Pareto optimality in fuzzy environments. Our results unify and generalize earlier work by Antczak and Mishra as well as demonstrate the power of generalized invexity in establishing optimality without requiring differentiability nor convexity. Several illustrative examples are included to demonstrate the applicability of the developed theory.