| 约束全局最优化的水平值估计算法 |
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| 引用本文： | 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 |
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| 作者姓名： | 彭拯 邬冬华 田蔚文 |
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| 作者单位： | 上海大学数学系,上海,200444;湖南理工学院数学系,湖南岳阳,414006;上海大学数学系,上海,200444 |
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| 基金项目： | 上海市重点学科项目，国家自然科学基金(No．10671117)项目资助． |
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| 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.
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| 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 |
| 修稿时间： | 2006-03-20 |
A LEVEL-VALUE ESTIMATION METHOD FOR SOLVING CONSTRAINED GLOBAL OPTIMIZATION |
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| Peng Zheng,Wu Donghua,Tian Weiwen. A LEVEL-VALUE ESTIMATION METHOD FOR SOLVING CONSTRAINED GLOBAL OPTIMIZATION[J]. Mathematica Numerica Sinica, 2007, 29(3): 293-304 |
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| Authors: | Peng Zheng Wu Donghua Tian Weiwen |
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| Affiliation: | 1.Department of Mathmaties, Shanghai University, Shanghai 200444, China;2.Department of Mathmaties, Hunan institute of technology and science, Yueyan9 414006, Hunan, China |
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| Abstract: | 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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| Keywords: | Constrained global optimization Level-value estimation method Variance function Discontinuous exact penalty function Newton's method Inexact Newton's method |
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