Second-order optimality conditions in locally Lipschitz multiobjective fractional programming problem with inequality constraints

Abstract

Our purpose, in this article, is to establish second-order optimality conditions for a second-order strict local Pareto minimum and a weak local Pareto minimum for a locally Lipschitz multiobjective fractional programming problem with inequality constraints. We do not require here the data to be second-order differentiable in any case. We first provide some basic calculus rules for the two extended-real-valued mappings defined on an open set of a Banach space. We second establish primal and dual Karush–Kuhn–Tucker second-order necessary optimality conditions to such problem. We third present second-order sufficient optimality conditions which are very near to a dual Karush–Kuhn–Tucker second-order necessary optimality condition. Some examples demonstrate the applicability of the obtained main results.