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约束全局最优化的水平值估计算法

彭拯,邬冬华,田蔚文,   

  1. 上海大学数学系,上海大学数学系,上海大学数学系 上海200444;湖南理工学院数学系,湖南岳阳414006,上海200444,上海200444
  • 出版日期:2007-03-14 发布日期:2007-03-14

彭拯,邬冬华,田蔚文,. 约束全局最优化的水平值估计算法[J]. 计算数学, 2007, 29(3): 293-304.

A LEVEL-VALUE ESTIMATION METHOD FOR SOLVING CONSTRAINED GLOBAL OPTIMIZATION

  1. Peng Zheng (Department of Mathmatics,Shanghai University,Shanghai 200444,China;Department of Mathmatics, Hunan institute of technology and science,Yueyang 414006,Hunan,China) Wu Donghua Tian Weiwen (Department of Mathmatics,Shanghai University,Shanghai 200444,China)
  • Online:2007-03-14 Published:2007-03-14
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 equai 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.
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