| 弱拟法锥条件下非凸优化问题的同伦算法 |
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| 引用本文： | 刘庆怀,张春阳,张树功. 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) |
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| 作者姓名： | 刘庆怀 张春阳 张树功 |
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| 作者单位： | 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 |
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| 基金项目： | 国家自然科学基金资助项目，吉林省自然科学基金资助项目 |
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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 |
Homotopy Method for Solving Nonconvex Optimization with Weak Quasi Normal Condition |
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| LIU QINGHUAI ZHANG CHUNYANG ZHANG SHUGONG. Homotopy Method for Solving Nonconvex Optimization with Weak Quasi Normal Condition[J]. Acta Mathematicae Applicatae Sinica, 2011, 34(6) |
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| Authors: | LIU QINGHUAI ZHANG CHUNYANG ZHANG SHUGONG |
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| Affiliation: | LIU QINGHUAI (Institute of Applied Mathematics,Changchun University of Technology,Changchun 130012) ZHANG CHUNYANG ZHANG SHUGONG |
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| 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 constrained non-convex programming program.For almost all the point in some feasible subset, 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. |
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| Keywords: | nonconvex optimization homotopy method interior point method weak qusi-normal cone condition |
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