"准"精确惩罚函数法的渐近性分析

1引言众所周知,罚函数法在最优化理论与数值计算中占据着极其重要的位置,作为求解约束优化问题的一类重要方法,在上世纪五、六十年代曾经历一次发展高潮．近十几年来,伴随着对数障碍函数法在内点法中取得的成功,罚函数法的研究又呈现出一个小高潮[2,3,4]．在罚函数方法里,精确惩罚函数法有着非常吸引人的性质,即,当罚参数大于某个有限门槛值时,仅通过求解单个无约束罚问题便可得到原问题的最优解,从而省去了一般罚函数法解系列无约束优化问题的工作量．

THE ASYMPTOTIC ANALYSIS OF QUASI-EXACT PENALTY FUNCTION METHOD

This paper dealth with analysis of the approximate exactness of quasiexact penalty function method in [1], and demonstration of the fact that the penalty problem and the original problem are approximately equivalent when the penalty parameter is larger than the threshold value for the Lee-exact penalty method. Moreover, the approximation error can be bounded by the smoothing parameter involved in the quasi-exact penalty function. On the basis of these results, a specific quasi-exact penalty algorithm is established, and for problems satisfying Mangasarian-Fromovitz constraint qualification, all iterates are shown to be feasible after a finite number of iterations. Thus, the main property of Lee-exact penalty function method is extended to the quasi-exact penalty function method.