混合变分不等式的变分原理  

Variational Principles for Mixed Variational Inequalities

作　　者：黄冬梅[1] 

机构地区：[1]西华师范大学数学与信息学院,四川南充637009

出　　处：《西华师范大学学报（自然科学版）》2016年第3期297-302,共6页Journal of China West Normal University(Natural Sciences)

基　　金：国家自然科学基金项目(11371015);教育部科学技术重点项目(211163);四川省青年科技基金(2012JQ0035)

摘　　要：描述并分析了有限维空间中混合变分不等式的变分原理,同时给出了混合变分不等式的解基于鞍点的刻画,最后,针对一些特殊情型给出了混合变分不等式问题基于经典优化问题的等价性刻画。因为线性,非线性补问题也可纳入混合变分不等式问题的框架,所以文章中得到的结果也可以直接用于这类问题。The theory of mixed variational inequality problems has wide applications in economics, finance, optimization and game theory. This paper describes and analyzes variational principles for the solution of mixed variational inequalities on closed convex sets in finite dimensional Euclidean spaces. A saddle point characterization of the so-lution is also given. Some special cases are also given to illustrate mixed variational inequalities. Since linear, and nonlinear complementarity problems may be framed as mixed variational inequalities, this theory also applies to such problems.

关 键 词：变分不等式 混合变分不等式 变分原理 

分 类 号：O221[理学—运筹学与控制论]