摘要
本文提出求解非线性极大极小问题的一种新的有效方法,称为凝聚函数法。通过利用最大熵原理构造复合的拉格朗日对偶问题,可以导出一个用于求解极大极小问题的凝聚函数。可以证明,该函数具有Lp模的一些类似性质,并且当所含参数趋于无穷大时,精确逼近最大值函数。文中提出一个利用这个凝聚函数作为目标函数的无约束优化算法。几个算例表明,该方法具有收敛稳定、算法简单及计算效率高等优点。
This paper presents a new and very efficient method, referred to as the aggregate function method, for solving nonlinear minimax problems. By employing the maximum entropy principle, the author has formulated a compound Lagrangean dual problem and derived the aggregate function as its solution. It can be shown that this function has some properties similar to those of Lp norm and approaches the maximum function as a controlling parameter tends to infinity. Thus the solution of a minimax problem can be found by only one iteration of unconstrained minimization of the aggregate function for a sufficient large parameter. Numerical examples show that the present method has advantages of stable convergence, easy implementation and high efficiency.
基金
国家自然科学基金
