| A MODIFIED VARIABLE-PENALTY ALTERNATING DIRECTIONS METHOD FOR MONOTONE VARIATIONAL INEQUALITIES |
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| 作者姓名： | Bing-shengHe Sheng-liWang HaiYang |
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| 作者单位： | [1]DepartmentofMathematics,NanjingUniversity,Nanjing210093,China [2]DepartmentofCivilEngineering,TheHongKongUniversityofScience~Technology,ClearWaterBay,Kowloon,HongKong |
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| 基金项目： | The first author was supported the NSFC grant 10271054,the third author was supported in part by the Hong Kong Research Grants Council through a RGC-CERG Grant (HKUST6203/99E) |
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| 摘 要： | Alternating directions method is one of the approaches for solving linearly constrained separate monotone variational inequalities. Experience on applications has shown that the number of iteration significantly depends on the penalty for the system of linearly constrained equations and therefore the method with variable penalties is advantageous in practice. In this paper, we extend the Kontogiorgis and Meyer method 12] by removing the monotonicity assumption on the variable penalty matrices. Moreover, we introduce a self-adaptive rule that leads the method to be more efficient and insensitive for various initial penalties. Numerical results for a class of Fermat-Weber problems show that the modified method and its self-adaptive technique are proper and necessary in practice.
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| 关 键 词： | 单调变分不等式 交替方向法 Fermat-Weber问题 特征值 收敛性 |
A MODIFIED VARIABLE-PENALTY ALTERNATING DIRECTIONS METHOD FOR MONOTONE VARIATIONAL INEQUALITIES |
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| Bing-shengHe Sheng-liWang HaiYang.A MODIFIED VARIABLE-PENALTY ALTERNATING DIRECTIONS METHOD FOR MONOTONE VARIATIONAL INEQUALITIES[J].Journal of Computational Mathematics,2003,21(4):495-504. |
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| Authors: | Bing-sheng He Sheng-li Wang |
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| Abstract: | Alternating directions method is one of the approaches for solving linearly constrained separate monotone variational inequalities. Experience on applications has shown that the number of iteration significantly depends on the penalty for the system of linearly constrained equations and therefore the method with variable penalties is advantageous in practice. In this paper, we extend the Kontogiorgis and Meyer method 12] by removing the monotonicity assumption on the variable penalty matrices. Moreover, we introduce a self-adaptive rule that leads the method to be more efficient and insensitive for various initial penalties. Numerical results for a class of Fermat-Weber problems show that the modified method and its self-adaptive technique are proper and necessary in practice. |
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| Keywords: | Monotone variational inequalities Alternating directions method Fermat-Weber problem |
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