求解极大极小问题的一种稳定的对数障碍函数法

给出求解极大极小问题的一种对数障碍函数法．为了消除牛顿方程的病态，本文引进Ｂｒｏｙｄｅｎ 和Ａｔｔｉａ 在求解约束优化问题时，为克服罚函数的病态所采取的一种策略，提高了算法的稳定性．对子问题的结束准则等对算法的效率有重要影响的技术细节，本文也进行了研究．

AN IMPROVED VERSION OF BARRIER FUNCTION METHOD FOR FINITE MINIMAX PROBLEMS

This paper presents an improved version of the inverse barrier function method proposed by Polak et al (see Mathematical Programming,1992) for finite minimax problems.In this method,the inverse barrier function is substituted by the logrithmic barrier function,and a stabilization technique,which was used in the penalty function method for constrained non linear programming by Broyden and Attia,is employed to eliminate the ill conditioning of the Newton type equation.Stopping criterion for sub problems and other techniques are studied in order to reduce the number of inner steps.Numerical experience shows that the algorithm proposed here is superior to the inverse barrier function method in sense of solution precision and function/derivative evaluation times.