变分不等式的极大熵函数方法  

Entropy Function Methods for Variational Inequality Problem

作　　者：傅白白[1] 

机构地区：[1]北京交通大学交通运输学院,北京100044

出　　处：《数学的实践与认识》2005年第8期84-88,共5页Mathematics in Practice and Theory

摘　　要：利用极大熵函数方法将不等式组及变分不等式的求解问题转化为近似可微优化问题,给出了不等式组及变分不等式问题近似解的可微优化方法,得到了不等式组和变分不等式问题的解集合的示性函数.An entropy function for inequalities and a Boltzmann entropy expression for the gap function of the variational inequality problem （VIP） are presented. The maximum entropy function approach for max-min problems is introduced to solve traditional inequalities. The solution of inequalities can be approached by getting the local minimum solution of a differentiable convex function optimization problem. The authors developed the concept of Shannon entropy function by employing prior distribution information and Boltzmann entropy concepts to obtain the maximum entropy function of the gap function for VIP. The VIP can also be solved by approaching differential optimization methods.

关 键 词：变分不等式 不等式组 极大熵函数 凸优化 变分不等式问题 函数方法 极大熵 优化问题 问题转化 示性函数 

分 类 号：O178[理学—数学] G633.62[理学—基础数学]