Second-order optimality conditions in locally Lipschitz multiobjective fractional programming problem with inequality constraints. (4th May 2023)

• Record Type: Journal Article
• Authors: Su, Tran Van; Hang, Dinh Dieu
• Is Part Of: Optimization. Volume 72:Number 5(2023)
• Page Start: 1171
• Page End: 1198
• Publication Date: 2023-05-04
• Subjects: Nonsmooth multiobjective fractional optimization -- Karush–Kuhn–Tucker type dual optimality conditions -- second-order strict local Pareto minimum -- second-order generalized directional derivatives -- Clarke's generalized derivative; 90C46 -- 91B50 -- 90C29 -- 49J52 -- 90C48; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.2002328
• Languages: English
• ISSNs: 0233-1934

Abstract

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.