One of the classical approaches in the analysis of a variational inequality problem is to transform it into an equivalent optimization problem via the notion of gap function. The gap functions are useful tools in deri...One of the classical approaches in the analysis of a variational inequality problem is to transform it into an equivalent optimization problem via the notion of gap function. The gap functions are useful tools in deriving the error bounds which provide an estimated distance between a specific point and the exact solution of variational inequality problem. In this paper, we follow a similar approach for set-valued vector quasi variational inequality problems and define the gap functions based on scalarization scheme as well as the one with no scalar parameter. The error bounds results are obtained under fixed point symmetric and locally α-Holder assumptions on the set-valued map describing the domain of solution space of a set-valued vector quasi variational inequality problem.展开更多
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
文摘One of the classical approaches in the analysis of a variational inequality problem is to transform it into an equivalent optimization problem via the notion of gap function. The gap functions are useful tools in deriving the error bounds which provide an estimated distance between a specific point and the exact solution of variational inequality problem. In this paper, we follow a similar approach for set-valued vector quasi variational inequality problems and define the gap functions based on scalarization scheme as well as the one with no scalar parameter. The error bounds results are obtained under fixed point symmetric and locally α-Holder assumptions on the set-valued map describing the domain of solution space of a set-valued vector quasi variational inequality problem.
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.
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
