Minimax型极值问题的扰动分析

Perturbed Analysis for Minimax Extreme Value Problem

本文将考虑以存在性为特例的Minimax型极值问题解集的扰动分析 .许多经济系统中的优化问题 ,可化为用单值非线性算子或多值算子形成约束条件的条件极值问题 .这一类问题又可通过Hamilton函数、Lagrange函数转化为适当乘积空间上二元函数f(x,y)的Mini sup解、Max inf解的存在性问题 .针对以上问题 ,本文研究了乘积Banach空间U×V上的函数f(x ,y)的极值问题 ,获得了线性扰动下Mini sup解、Max inf解的存在性结果、连续性质和解的表现形式 ,并导出了Conservative解和鞍点的相关结论 .

This paper deals with perturbed analysis for Minimax extreme value problem which takes the existence for special example. All know that most of the optimization of economic system can be converted into conditional extreme value problem which takes nonlinear operator or multi operator as constraints. The latter can be converted into the existence of Max inf solution and Mini sup solution of function f(x,y) defined on proper conduct spaces by means of Hamilton function and Lagrange function. The extreme value problem of function f(x,y) defined on product Banach space U×V is discussed. Some existence theorems, continuity and the expressions of Max inf solution and Min sup solution under linear perturbation are obtained. As a corollary, some results with respect to conservative solution and saddle point are obtainted.