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应用数学学报  2011, Vol. 34 Issue (6): 996-1006    DOI:
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弱拟法锥条件下非凸优化问题的同伦算法
刘庆怀1, 张春阳2, 张树功2
1. 长春工业大学应用数学所, 长春 130012;
2. 吉林大学数学研究所, 长春 130012
Homotopy Method for Solving Nonconvex Optimization with Weak Quasi Normal Condition
LIU Qinghuai1, ZHANG Chunyang2, ZHANG Shugong2
1. Institute of Applied Mathematics, Changchun University of Technology, Changchun 130012;
2. Institute of mathematics, Jilin University, Changchun 130012
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摘要 本文给出弱拟法锥条件的定义, 并针对非线性组合同伦方程, 得到在弱拟法锥条件下求解约束非凸优化问题的同伦内点算法. 证明了该算法对于可行域的某个子集中几乎所有的点, 同伦路径存在, 并且同伦路径收敛于问题的K-K-T点. 通过数值例子验证了该算法是有效的.  
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关键词非凸优化   同伦算法   内点法   弱拟法锥条件     
Abstract: In this paper, we define the weak qusi-normal cone condition and consider the nonlinear homotopy equation under the weak quasi-normal cone condition to solve con- strained non-convex programming program. For almost all the point in some feasible sub- set, the existence of the homotopy path is proved and the homotopy path converges to the K-K-T point. Numerical examples are presented to show the effectiveness of the algorithm.  
Key wordsnonconvex optimization   homotopy method   interior point method   weak qusi-normal cone condition   
收稿日期: 2006-01-09;
基金资助:

国家自然科学基金资助项目(10771020), 吉林省自然科学基金资助项目(20101597).

引用本文:   
. 弱拟法锥条件下非凸优化问题的同伦算法[J]. 应用数学学报, 2011, 34(6): 996-1006.
. Homotopy Method for Solving Nonconvex Optimization with Weak Quasi Normal Condition[J]. Acta Mathematicae Applicatae Sinica, 2011, 34(6): 996-1006.
 
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