Generalized asymptotic functions in nonconvex multiobjective optimization problems. (3rd August 2017)

• Record Type: Journal Article
• Authors: Lara, F.
• Is Part Of: Optimization. Volume 66:Number 8(2017)
• Page Start: 1259
• Page End: 1272
• Publication Date: 2017-08-03
• Subjects: Quasiconvexity -- asymptotic functions -- second-order asymptotic cones -- nonconvex vector optimization -- linear fractional programming; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2016.1235162
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, we use generalized asymptotic functions and second-order asymptotic cones to develop a general existence result for the nonemptiness of the proper efficient solution set and a sufficient condition for the domination property in nonconvex multiobjective optimization problems. A new necessary condition for a point to be efficient or weakly efficient solution is given without any convexity assumption. We also provide a finer outer estimate for the asymptotic cone of the weakly efficient solution set in the quasiconvex case. Finally, we apply our results to the linear fractional multiobjective optimization problem.