集值拟变分不等式的间隙函数

利用有限维空间中拟变分不等式理论,讨论严格凸光滑赋范线性空间集值映射的拟变分不等式.通过估计原理,引入集值拟变分不等式的间隙函数,给出间隙函数的有关性质,建立它的误差边界,得到间隙函数在T为弱*紧值的μ-强伪单调集值映射,S在不动点处为对称或局部α-Hlder集值映射条件下的误差估计,并给出在广义纳什均衡问题中的应用.

Gap Function for Set-valued Quasi-variational Inequalities

By using the relevant theorem of quasi-variational inequalities in the finite dimensional space,the quasi-variational inequalities for set-valued maps in the strongly convex smooth linear norm space were established.Gap function for set-valued quasi-variational inequalities was introduced by an axiomatic approach and the properties of the gap function were provided.Then error bounds of the gap function were given and error estimates were obtained under the condition that T was μ-strong pseudomonotonous set-valued map with nonempty compact values and S was fixead point symmetric or locally α-Holder set-valued map.Applications to generalized Nash equilibrium problems were considered.