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,we introduce a new directional derivative and subgradient of set-valued mappings by using a nonlinear scalarizing function.We obtain some properties of directional derivative and subgradient for cone-con...In this paper,we introduce a new directional derivative and subgradient of set-valued mappings by using a nonlinear scalarizing function.We obtain some properties of directional derivative and subgradient for cone-convex set-valued mappings.As applications,we present necessary and sufficient optimality conditions for set optimization problems and show that the local weak l-minimal solutions of set optimization problems are the global weak l-minimal solutions of set optimization problems under the assumption that the objective mapping is cone-convex.展开更多
In this paper,under some suitable assumptions without any involving information on the solution set,we give some sufficient conditions for the upper semicontinuity,lower semicontinuity,and closedness of the solution s...In this paper,under some suitable assumptions without any involving information on the solution set,we give some sufficient conditions for the upper semicontinuity,lower semicontinuity,and closedness of the solution set mapping to a parametric set optimization problem with possible less order relation.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.
基金supported by the National Natural Science Foundation of China(11801257).
文摘In this paper,we introduce a new directional derivative and subgradient of set-valued mappings by using a nonlinear scalarizing function.We obtain some properties of directional derivative and subgradient for cone-convex set-valued mappings.As applications,we present necessary and sufficient optimality conditions for set optimization problems and show that the local weak l-minimal solutions of set optimization problems are the global weak l-minimal solutions of set optimization problems under the assumption that the objective mapping is cone-convex.
基金the National Natural Science Foundation of China(No.11426055)the Science and Technology Research Project of Chongqing Municipal Education Commission(No.KJ1500419)+1 种基金the Basic and Advanced Research Project of Chongqing Science and Technology Commission(No.cstc2014jcyjA00044)the Doctor Start-up Foundation of Chongqing University of Posts and Telecommunications(No.A2014-15).
文摘In this paper,under some suitable assumptions without any involving information on the solution set,we give some sufficient conditions for the upper semicontinuity,lower semicontinuity,and closedness of the solution set mapping to a parametric set optimization problem with possible less order relation.
