Inclusion functions and global optimization II
Inclusion functions and global optimization II
复制标题
包含函数和全局优化 II
作者：
Ramon E. Moore;H. Ratschek
本文讨论了摩尔、伊博、Ichida、藤井和汉森等人求解全局无约束优化问题的算法。这些算法已经在计算机上进行了尝试，但对它们的收敛性进行了彻底的理论讨论。讨论开始于本文的第一部分（数学规划33（1985）300-317），其中研究了全局最小值的收敛性。本文关注的是这些算法的不同行为时，它们被用于确定全球最低点。这些算法的解集可以是全局极小点集G的子集，G的超集，或者恰好是G。该算法适用于一个非常一般的一类函数：函数是连续的，并有适当的包含函数。全局最小点的数量可以是无限的。
This paper discusses algorithms of Moore, Skelboe, Ichida, Fujii and Hansen for solving the global unconstrained optimization problem. These algorithms have been tried on computers, but a thorough theoretical discussion of their convergence properties has been missing. The discussion was started in part I of this paper (Mathematical Programming 33 (1985) 300–317) where the convergence to the global minimum was studied. The present paper is concerned with the different behaviours of these algorithms when they are used for the determination of global minimum points. The solution sets of the algorithms can be a subset of the set of global minimum points,G, a superset ofG, or exactlyG. The algorithms are applicable to a very general class of functions: functions which are continuous, and have suitable inclusion functions. The number of global minimum points can be infinite.