This paper deals with Henig globally efficiency in vector optimization involving generalized cone-preinvex set-valued mapping. Some properties of generalized cone-preinvex set-valued map are derived. It also disclose ...This paper deals with Henig globally efficiency in vector optimization involving generalized cone-preinvex set-valued mapping. Some properties of generalized cone-preinvex set-valued map are derived. It also disclose the closed relationships between Henig globally efficiency of generalized conepreinvex set-valued optimization problem and Henig globally efficiency of a kind of vector variational inequality.展开更多
In this paper, the authors introduce and study system of generalized vector variational inequalities. Under suitable conditions, the existence of solutions for system of generalized vector variational inequalities is ...In this paper, the authors introduce and study system of generalized vector variational inequalities. Under suitable conditions, the existence of solutions for system of generalized vector variational inequalities is presented by Kakutani-Fan-Glicksberg fixed point theorem.展开更多
A class of bilevel variational inequalities(shortly(BVI))with hierarchical nesting structure is firstly introduced and investigated.The relationship between(BVI)and some existing bilevel problems are presented.Subseq...A class of bilevel variational inequalities(shortly(BVI))with hierarchical nesting structure is firstly introduced and investigated.The relationship between(BVI)and some existing bilevel problems are presented.Subsequently,the existence of solution and the behavior of solution sets to(BVI)and the lower level variational inequality are discussed without coercivity.By using the penalty method,we transform(BVI)into one-level variational inequality,and establish the equivalence between(BVI)and the one-level variational inequality.A new iterative algorithm to compute the approximate solutions of(BVI)is also suggested and analyzed.The convergence of the iterative sequence generated by the proposed algorithm is derived under some mild conditions.Finally,some relationships among(BVI),system of variational inequalities and vector variational inequalities are also given.展开更多
基金supported by the Natural Science Foundation of China under Grant No.11361001Ministry of Education Science and technology key projects under Grant No.212204+1 种基金the Natural Science Foundation of Ningxia under Grant No.NZ12207the Science and Technology key project of Ningxia institutions of higher learning under Grant No.NGY2012092
文摘This paper deals with Henig globally efficiency in vector optimization involving generalized cone-preinvex set-valued mapping. Some properties of generalized cone-preinvex set-valued map are derived. It also disclose the closed relationships between Henig globally efficiency of generalized conepreinvex set-valued optimization problem and Henig globally efficiency of a kind of vector variational inequality.
文摘In this paper, the authors introduce and study system of generalized vector variational inequalities. Under suitable conditions, the existence of solutions for system of generalized vector variational inequalities is presented by Kakutani-Fan-Glicksberg fixed point theorem.
基金This work was supported partly by the National Natural Science Foundation of China (70501015, 70321001). The original version was presented at the Congress of the IFSR2005
基金This work was supported by the Natural Science Foundation of China(Nos.71171150,11201039)the Doctor Fund of Southwest University(No.SWU113037)+1 种基金the Fundamental Research Funds for the Central Universities(No.XDJK2014C073)The authors wish to thank the anonymous referees and associated editor for their very careful and valuable comments which led to an improved presentation of this manuscript.
文摘A class of bilevel variational inequalities(shortly(BVI))with hierarchical nesting structure is firstly introduced and investigated.The relationship between(BVI)and some existing bilevel problems are presented.Subsequently,the existence of solution and the behavior of solution sets to(BVI)and the lower level variational inequality are discussed without coercivity.By using the penalty method,we transform(BVI)into one-level variational inequality,and establish the equivalence between(BVI)and the one-level variational inequality.A new iterative algorithm to compute the approximate solutions of(BVI)is also suggested and analyzed.The convergence of the iterative sequence generated by the proposed algorithm is derived under some mild conditions.Finally,some relationships among(BVI),system of variational inequalities and vector variational inequalities are also given.
