摘要
本文针对约束全局最优化问题,定义并研究了约束水平集上的方差函数,利用牛顿切线法求解方差方程的最大根构造出一种全局优化的水平值估计算法,并基于数论中一致分布佳点集求数值积分的方法建立了它的实现算法,验证了实现算法满足不精确牛顿算法的收敛性条件,从而证明了实现算法的收敛性.初步的数值实验说明了算法的有效性.
In this paper, we propose a level-value estimation method for solving constrained global optimization problem. By defining a variance function on the constrained level-set and investigating its properties, applying Newton＇s method to calculate the root of the equation that the variance function be equal to zero, we establish the level-value estimation method. By using uniform distribution good points set in number-theoretic technique to calculate integral, we construct the implementable algorithm and prove its convergence by showing it satisfies the convergent condition of inexact Newton＇s method. The efficiency of this algorithm is testified by numerical experimentation.
出处
《计算数学》
CSCD
北大核心
2007年第3期293-304,共12页
Mathematica Numerica Sinica
基金
上海市重点学科项目
国家自然科学基金(No.10671117)项目资助.
关键词
约束全局最优化
水平值估计算法
方差函数
非连续精确罚函数
牛顿法
不精确牛顿法
Constrained global optimization, Level-value estimation method, Variance function, Discontinuous exact penalty function, Newton＇s method, Inexact Newton＇s method
