Steepest descent method with a generalized Armijo search to solve quasiconvex fuzzy optimization problems under granular differentiability

Abstract

In this paper, we study the steepest descent method for unconstrained optimization problems involving quasiconvex fuzzy objective functions under granular differentiability. We introduce a class of granular quasiconvex and pseudoconvex functions, referred to as gr-quasiconvexity and gr-pseudoconvexity. Key properties of these functions and their interrelations are discussed. Leveraging the theory of quasi-Fej$\acute{e}$r convergence, we prove that the sequence generated by the steepest descent method with a generalized Armijo search converges completely to a granular stationary point of the fuzzy optimization problem. Several numerical examples are provided to demonstrate the effectiveness of the proposed approach. Additionally, a potential application in finance is considered and solved using our method.