一种修正的求总极值的积分-水平集方法的实现算法收敛性

AN ALGORITHM OF MODIFIED INTREGRAL-LEVEL SET METHOD FOR SOLVING GLOBAL OPTIMIZATION

１９７８年，郑权等提出了一个积分型求总极值的概念性算法及Ｍｏｎｔｅ－Ｃａｒｌｏ随机投点的实现算法，给出了概念性算法的总极值存在的充分必要条件，但是其实现算法收敛性仍未解决。１９９６年，张连生等给出了离散均值－水平集的实现算法，并证明了它的收敛性．本文给出修正的积分－水平集方法，用一致分布的数值积分逼近水平集构造实现算法，并证明了算法的收敛性．

In 1978, Zheng proposed a conceptual algorithm of integral global optimization and implementable approach by Monte-Carlo method, the convergence of this algorithm is still unsolved. In 1996, Zhang presented a practical algorithm of mean-level method, and proved its convergence. In this papers we give a modified integral-level method and construct an implementable algorithm by using uniformly distributed numerical integration which approximates the level set. We also show that this algorithm is convergent.