不等式的间隙函数

Gap Functions of a Kind of Hartman-Stampacchia Mutivalued Vector Variational-like Inequalities

摘要

摘要:间隙函数是将变分不等式转化为优化问题的有力工具,在变分不等式解的非空性、解的稳定性研究中被广泛使用．在研究强Hartman-Stampacchia型集值向量似变分不等式(SHSVL)和弱Hartman-Stampacchia型集值向量似变分不等式(WHSVL)的基础上,用数量化方法得到具有集值映射的SHSVL和WHSVL的间隙函数．

Abstract:Gap function is a powerful tool for translating variational inequalities into optimization problems, and is widely used to research the nonempty and the stability of variational inequality results. The strong Hartman and Stampacchia mutivalued vector variational-like inequality (SHSVL for short) and the weak Hartman and Stampacchia mutivalued vector variational-like inequality (WHSVL for short) are investigated. Furthermore, the gap functions of SHSVL and WHSVL that have mutivalued mapping are discussed by means of quantification.