This paper mainly investigates the semicontinuity of solution mappings for set optimization problems under a partial order set relation instead of upper and lower set less order relations. To this end, we propose two ...This paper mainly investigates the semicontinuity of solution mappings for set optimization problems under a partial order set relation instead of upper and lower set less order relations. To this end, we propose two types of monotonicity definition for the set-valued mapping introduced by two nonlinear scalarization functions which are presented by these partial order relations. Then, we give some sufficient conditions for the semicontinuity and closedness of solution mappings for parametric set optimization problems. The results presented in this paper are new and extend the main results given by some authors in the literature.展开更多
In this paper, a characterization of tightly properly efficient solutions of set-valued optimization problem is obtained. The concept of the well-posedness for a special scalar problem is linked with the tightly prope...In this paper, a characterization of tightly properly efficient solutions of set-valued optimization problem is obtained. The concept of the well-posedness for a special scalar problem is linked with the tightly properly efficient solutions of set-valued optimization problem.展开更多
This paper deals with higher-order optimality conditions and duality theory for approximate solutions in vector optimization involving non-convex set-valued maps.Firstly,under the assumption of near cone-subconvexlike...This paper deals with higher-order optimality conditions and duality theory for approximate solutions in vector optimization involving non-convex set-valued maps.Firstly,under the assumption of near cone-subconvexlikeness for set-valued maps,the higher necessary and sufficient optimality conditions in terms of Studniarski derivatives are derived for local weak approximate minimizers of a set-valued optimization problem.Then,applications to Mond-Weir type dual problem are presented.展开更多
文摘This paper mainly investigates the semicontinuity of solution mappings for set optimization problems under a partial order set relation instead of upper and lower set less order relations. To this end, we propose two types of monotonicity definition for the set-valued mapping introduced by two nonlinear scalarization functions which are presented by these partial order relations. Then, we give some sufficient conditions for the semicontinuity and closedness of solution mappings for parametric set optimization problems. The results presented in this paper are new and extend the main results given by some authors in the literature.
文摘In this paper, a characterization of tightly properly efficient solutions of set-valued optimization problem is obtained. The concept of the well-posedness for a special scalar problem is linked with the tightly properly efficient solutions of set-valued optimization problem.
基金supported by Natural Science Foundation of China government under Grant No.11861002Natural Science Foundation of Ningxia under Grant No.NZ17112+3 种基金First-Class Disciplines Foundation of Ningxia under Grant No.NXYLXK2017B09The Key Project of North Minzu University under Grant No.ZDZX201804Graduate Innovation Project of North Minzu University No.YCX19122Nonlinear analysis and financial optimization research center of North Minzu University
文摘This paper deals with higher-order optimality conditions and duality theory for approximate solutions in vector optimization involving non-convex set-valued maps.Firstly,under the assumption of near cone-subconvexlikeness for set-valued maps,the higher necessary and sufficient optimality conditions in terms of Studniarski derivatives are derived for local weak approximate minimizers of a set-valued optimization problem.Then,applications to Mond-Weir type dual problem are presented.
