线性等式约束连续型minimax问题的区间算法

Interval Algorithm for a Class of Constinuous Minimax Problems with the Constraint Condition of Linear Equality

研究线性等式约束连续型minimax问题,其中目标函数为Lipschitz连续函数,基于线性约束函数的区间迭代运算、区域二分原则和无解区域删除原则,建立了求解线性等式约束连续型minimax问题的区间算法,证明了算法的相关定理,给出了数值算例,该算法保证求出问题的整体解,且是可靠和有效的.

This paper describes a class of continuous minimax problems with the constraint condition of linear equality, in which the objective functions are Lipschitz continuous. Based on the interval iterative computations of the linear constrained function, the region bisection method and region deletion testing rules, a interval algorithm is established. The relevant properties are proved. The method guarantees that the global solutions of minimax problems are obtained. The method is proved to be reliable and efficient by numerical results.