DUALITY THEORY FOR MULTIOBJECTIVE OPTIMIZATION PROBLEM WITH INVEXITY ASSUMPTIONS

Abstract

The study of multiobjective optimization problems often involves dealing with interval-valued objective functions, which represent uncertainty in real-world applications. This abstract presents an examination of multiobjective interval-valued optimization problems where the objective functions are invex, a generalization of convexity. The paper investigates the duality theory related with these types of problems, exploring how dual formulations can provide bounds and approximate solutions also insights into the feasibility and optimality of the original problem. By using invexity, we extend traditional convex optimization technique to handle interval-valued objectives, thus expanding the applicability of duality results. This study aims to develop theoretical foundations for solving these difficult problems, with a focus on characterizing optimal solutions and exploring their dual relationships.