Benson's algorithm for nonconvex multiobjective problems via nonsmooth Wolfe duality

Abstract

‎In this paper‎, ‎we propose an algorithm to obtain an approximation set of the (weakly) nondominated points of nonsmooth multiobjective optimization problems with equality and inequality constraints‎. ‎We use an extension of the Wolfe duality to construct the separating hyperplane in Benson's outer algorithm for multiobjective programming problems with subdifferentiable functions‎. ‎We also formulate an infinitive approximation set of the (weakly) nondominated points of biobjective optimization problems‎. ‎Moreover‎, ‎we provide some numerical examples to illustrate the advantage of our algorithm.