In this paper, two kinds of parametric generalized vector quasi-equilibrium problems are introduced and the relations between them are studied. The upper and lower semicontinuity of their solution sets to parameters a...In this paper, two kinds of parametric generalized vector quasi-equilibrium problems are introduced and the relations between them are studied. The upper and lower semicontinuity of their solution sets to parameters are investigated.展开更多
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 note studies the optimality conditions of vector optimization problems involving generalized convexity in locally convex spaces. Based upon the concept of Dini set-valued directional derivatives, the necessary an...This note studies the optimality conditions of vector optimization problems involving generalized convexity in locally convex spaces. Based upon the concept of Dini set-valued directional derivatives, the necessary and sufficient optimality conditions are established for Henig proper and strong minimal solutions respectively in generalized preinvex vector optimization problems.展开更多
By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established...By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.展开更多
By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established...By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.展开更多
In this article, we study Levitin-Polyak type well-posedness for generalized vector equilibrium problems with abstract and functional constraints. Criteria and characterizations for these types of well-posednesses are...In this article, we study Levitin-Polyak type well-posedness for generalized vector equilibrium problems with abstract and functional constraints. Criteria and characterizations for these types of well-posednesses are given.展开更多
A new class of bilcvel generalized mixed equilibrium problems involving setvalued mappings is introduced and studied in a real Banach space. By using the auxiliary principle technique, new iterative algorithms for sol...A new class of bilcvel generalized mixed equilibrium problems involving setvalued mappings is introduced and studied in a real Banach space. By using the auxiliary principle technique, new iterative algorithms for solving the generalized mixed equilibrium problems and bilevel generalized mixed equilibrium problems involving set-valued mappings are suggested and analyzed. Existence of solutions and strong convergence of the iterative sequences generated by the algorithms are proved under quite mild conditions. The behavior of the solution set of the generalized mixed equilibrium problems and bilevel generalized mixed equilibrium problems is also discussed. These results are new and generalize some recent results in this field.展开更多
In this paper, firstly, a new notion of generalized cone convex set-valued map is introduced in real normed spaces. Secondly, a property of the generalized cone convex set-valued map involving the contingent epideriva...In this paper, firstly, a new notion of generalized cone convex set-valued map is introduced in real normed spaces. Secondly, a property of the generalized cone convex set-valued map involving the contingent epiderivative is obtained. Finally, as the applications of this property, we use the contingent epiderivative to establish optimality conditions of the set-valued optimization problem with generalized cone convex set-valued maps in the sense of Henig proper efficiency. The results obtained in this paper generalize and improve some known results in the literature.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
The concept of a cone subarcwise connected set-valued map is introduced. Several examples are given to illustrate that the cone subarcwise connected set-valued map is a proper generalization of the cone arcwise connec...The concept of a cone subarcwise connected set-valued map is introduced. Several examples are given to illustrate that the cone subarcwise connected set-valued map is a proper generalization of the cone arcwise connected set-valued map, as well as the arcwise connected set is a proper generalization of the convex set,respectively. Then, by virtue of the generalized second-order contingent epiderivative, second-order necessary optimality conditions are established for a point pair to be a local global proper efficient element of set-valued optimization problems. When objective function is cone subarcwise connected, a second-order sufficient optimality condition is also obtained for a point pair to be a global proper efficient element of set-valued optimization problems.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
基金The NSF(10871226) of Chinathe NSF(ZR2009AL006) of Shandong Province
文摘In this paper, two kinds of parametric generalized vector quasi-equilibrium problems are introduced and the relations between them are studied. The upper and lower semicontinuity of their solution sets to parameters are investigated.
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.
文摘This note studies the optimality conditions of vector optimization problems involving generalized convexity in locally convex spaces. Based upon the concept of Dini set-valued directional derivatives, the necessary and sufficient optimality conditions are established for Henig proper and strong minimal solutions respectively in generalized preinvex vector optimization problems.
文摘By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.
文摘By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.
基金supported by the National Science Foundation of China and Shanghai Pujian Program
文摘In this article, we study Levitin-Polyak type well-posedness for generalized vector equilibrium problems with abstract and functional constraints. Criteria and characterizations for these types of well-posednesses are given.
基金supported by the Scientific Research Fun of Sichuan Normal University (11ZDL01)the Sichuan Province Leading Academic Discipline Project (SZD0406)
文摘A new class of bilcvel generalized mixed equilibrium problems involving setvalued mappings is introduced and studied in a real Banach space. By using the auxiliary principle technique, new iterative algorithms for solving the generalized mixed equilibrium problems and bilevel generalized mixed equilibrium problems involving set-valued mappings are suggested and analyzed. Existence of solutions and strong convergence of the iterative sequences generated by the algorithms are proved under quite mild conditions. The behavior of the solution set of the generalized mixed equilibrium problems and bilevel generalized mixed equilibrium problems is also discussed. These results are new and generalize some recent results in this field.
基金supported by the National Nature Science Foundation of China(11431004,11471291)the General Project of Chongqing Frontier and Applied Foundation Research(cstc2015jcyj A00050)the Key Project of Chongqing Frontier and Applied Foundation Research(cstc2017jcyj BX0055,cstc2015jcyj BX0113)
文摘In this paper, firstly, a new notion of generalized cone convex set-valued map is introduced in real normed spaces. Secondly, a property of the generalized cone convex set-valued map involving the contingent epiderivative is obtained. Finally, as the applications of this property, we use the contingent epiderivative to establish optimality conditions of the set-valued optimization problem with generalized cone convex set-valued maps in the sense of Henig proper efficiency. The results obtained in this paper generalize and improve some known results in the literature.
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.
基金Supported by the National Natural Science Foundation of China Grant 11461044the Natural Science Foundation of Jiangxi Province(20151BAB201027)the Science and Technology Foundation of the Education Department of Jiangxi Province(GJJ12010)
文摘The concept of a cone subarcwise connected set-valued map is introduced. Several examples are given to illustrate that the cone subarcwise connected set-valued map is a proper generalization of the cone arcwise connected set-valued map, as well as the arcwise connected set is a proper generalization of the convex set,respectively. Then, by virtue of the generalized second-order contingent epiderivative, second-order necessary optimality conditions are established for a point pair to be a local global proper efficient element of set-valued optimization problems. When objective function is cone subarcwise connected, a second-order sufficient optimality condition is also obtained for a point pair to be a global proper efficient element of set-valued optimization problems.
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.
