全局最优化问题的一种确定性算法

提出了一种求解全局最优化问题的确定性算法,它属于求解带有给定精度的全局最优解的覆盖法.原理是排除区域,即检查出不包含全局最优解的子区域,并从深入研究中排除出去.对某些特殊类型函数,将区域作一致网格覆盖,通过计算结点处的函数值逐次去除函数值较大的区域,保留函数值较小的区域,最终得到达到要求精度的全局极小值.算法要求函数的Hesse矩阵特征值的界可估计,并利用该界确定算法的终止条件.最后给出了数值例子.

Deterministic Algorithm for Global Optimization

A deterministic algorithm for global optimization is presented.The algorithm is one of covering methods which find the global minimum with required degree of accuracy.The principle of the algorithm is region cutting.The regions which the global minimum is not included are found and cut from deeply research.When we research some special functions,we can make a consistent net covering on the region.By calculating the function evaluations of the nodes,the regions in which function evaluation is larger are successively cut and the regions in which function evaluation is smaller are remained.At last,the global minimum is known to the required degree of accuracy.The algorithm requires the bound of the eigenvalues of the Hessian can be estimated and uses the bound to determine the stopping rule.Several numerical examples are presented at the end of the paper.