On the optimality conditions for D.C. vector optimization problems. (3rd July 2022)

• Record Type: Journal Article
• Authors: Khazayel, Bahareh; Farajzadeh, Ali
• Is Part Of: Optimization. Volume 71:Number 7(2022)
• Page Start: 2033
• Page End: 2045
• Publication Date: 2022-07-03
• Subjects: Convex mapping -- optimality conditions -- local weak minimal solution -- subdifferential -- minimal point; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1847109
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, by using the notions of approximate pseudo-dissipativity, strong subdifferential and epsilon-subdifferential, we present sufficient optimality conditions for an epsilon-weak local Pareto minimal solution and an epsilon-local Pareto minimal solution of a vector optimization problem, where its objective function and constraint set are in the form of differences of two vector-valued convex maps, respectively. Then, an application of the given result is obtained for vector fractional programming. Also, some comments are given on two recently published papers presented by Guo and Li [Optimality conditions for vector optimization problems with difference of convex maps. J Optim Theory Appl. 2014;162:821–844] and Gadhi and Metrane [Sufficient optimality condition for vector optimization problems under D.C. J Glob Optim. 2004;28:55–66].