KKT conditions for optimization with generalized invex fuzzy functions

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.