In this paper, we introduce the concept of a (weak) minimizer of order k for a nonsmooth vector optimization problem over cones. Generalized classes of higher-order cone-nonsmooth (F, ρ)-convex functions are introduc...In this paper, we introduce the concept of a (weak) minimizer of order k for a nonsmooth vector optimization problem over cones. Generalized classes of higher-order cone-nonsmooth (F, ρ)-convex functions are introduced and sufficient optimality results are proved involving these classes. Also, a unified dual is associated with the considered primal problem, and weak and strong duality results are established.展开更多
This paper deals with multiobjective programming problems with support functions under （G, C, ρ）-convexity assumptions. Not only sufficient but also necessary optimality conditions for this kind of multiobjective p...This paper deals with multiobjective programming problems with support functions under （G, C, ρ）-convexity assumptions. Not only sufficient but also necessary optimality conditions for this kind of multiobjective programming problems are established from a viewpoint of （G, C, ρ）-convexity. When the sufficient conditions are utilized, the corresponding duality theorems are derived for general Mond-Weir type dual program.展开更多
The aim of this paper is to prove that the average function of a trigonometrically ρ-convex function is trigonometrically ρ-convex. Furthermore, we show the existence of support curves implies the trigonometric ρ-c...The aim of this paper is to prove that the average function of a trigonometrically ρ-convex function is trigonometrically ρ-convex. Furthermore, we show the existence of support curves implies the trigonometric ρ-convexity, and prove an extremum property of this function.展开更多
文摘In this paper, we introduce the concept of a (weak) minimizer of order k for a nonsmooth vector optimization problem over cones. Generalized classes of higher-order cone-nonsmooth (F, ρ)-convex functions are introduced and sufficient optimality results are proved involving these classes. Also, a unified dual is associated with the considered primal problem, and weak and strong duality results are established.
基金supported by the Natural Science Foundation of Guangdong Province under Grant No.S2013010013101the Science Foundations of Hanshan Normal University under Grant Nos.QD20131101and LZ201403
文摘This paper deals with multiobjective programming problems with support functions under （G, C, ρ）-convexity assumptions. Not only sufficient but also necessary optimality conditions for this kind of multiobjective programming problems are established from a viewpoint of （G, C, ρ）-convexity. When the sufficient conditions are utilized, the corresponding duality theorems are derived for general Mond-Weir type dual program.
文摘The aim of this paper is to prove that the average function of a trigonometrically ρ-convex function is trigonometrically ρ-convex. Furthermore, we show the existence of support curves implies the trigonometric ρ-convexity, and prove an extremum property of this function.
