The cluster problem in multivariate global optimization
The cluster problem in multivariate global optimization
复制标题
多元全局优化中的聚类问题
DOI：
10.1007/bf01096455
复制
发表时间：
1994
影响因子：
1.8
通讯作者：
R. B. Kearfott
中科院分区：
文献类型：
--
作者：
Kaisheng Du;R. B. Kearfott
We consider branch and bound methods for enclosing all unconstrained global minimizers of a nonconvex nonlinear twice-continuously differentiable objective function. In particular, we consider bounds obtained with interval arithmetic, with the “midpoint test,” but no acceleration procedures. Unless the lower bound is exact, the algorithm without acceleration procedures in general gives an undesirable cluster of boxes around each minimizer. In a previous paper, we analyzed this problem for univariate objective functions. In this paper, we generalize that analysis to multi-dimensional objective functions. As in the univariate case, the results show that the problem is highly related to the behavior of the objective function near the global minimizers and to the order of the corresponding interval extension.
