非线性等式约束离散minimax问题的区间极大熵算法

The Interval Maximum Entropy Method for the Discrete Minimax Problem of Nonlinear Equality Constrain

研究了求解非线性等式约束离散mimimax问题的区间算法,其中目标函数和约束函数都是C1类函数.利用极大熵函数和罚函数将问题转化为无约束可微优化问题,借助广义Krawczyk-Hansen算子建立了约束函数的区间迭代;讨论了极大熵函数和罚函数的区间扩张,证明了收敛性等性质,给出了无解区域删除原则,建立了区间极大熵算法.大量数值算例表明该算法是可靠和有效的.

This paper is concerned with the interval algorithm for the discrete minimax of nonlinear equality constrain , in which the objective function and constrained function are all C1 function. This problem can be converted into an unconstrained optimized differential by means of maximum entropy function and penalty function. On the basis of general Krawczyk-Hansen Operator, the interval iteration of the constrained functions are established; the interval extension of maximum entropy function is discussed; convergence is proved; region deletion rules are supplied and the algorithm of interval maximum entropy has been set up. The method is proved to be reliable and efficient by numerical result.