| 均衡及约束凸优化问题公共解的一般迭代算法 |
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| 引用本文： | 田明,刘磊. 均衡及约束凸优化问题公共解的一般迭代算法[J]. 中国科学:数学, 2013, 43(4): 365-381. DOI: 10.1360/012012-29 |
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| 作者姓名： | 田明 刘磊 |
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| 作者单位： | 中国民航大学理学院, 天津300300 |
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| 基金项目： | 中央高校基本科研业务费专项资金(批准号:ZXH2012K001)和中国民航大学应用基础研究(批准号:2012KYM03)资助项目 |
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| 摘 要： | 梯度投影法在解决约束凸极小化问题中起到了重要的作用. 基于Tian的一般迭代算法, 本文将梯度投影法和平均算子方法相结合, 首次提出隐式和显式的复合迭代算法, 寻求均衡问题和约束凸极小化问题的公共解. 在适当条件下, 获得了强收敛定理.
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| 关 键 词： | 均衡问题 约束凸优化问题 变分不等式 |
A general iterative algorithm for finding a common solution of equilibrium and constrained convex minimization problems |
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| TIAN Ming,LIU Lei. A general iterative algorithm for finding a common solution of equilibrium and constrained convex minimization problems[J]. Scientia Sinica Mathemation, 2013, 43(4): 365-381. DOI: 10.1360/012012-29 |
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| Authors: | TIAN Ming LIU Lei |
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| Abstract: | The gradient-projection algorithm (GPA) plays an important role in solving constrained convex mini-mization problems. Based on Tian''s method, we combine GPA and averaged mapping approach to propose implicit and explicit composite iterative algorithms for finding a common solution of an equilibrium and a constrained convex minimization problem for the first time in this paper. Under suitable conditions, strong convergence theorems are obtained. |
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| Keywords: | equilibrium problem constrained convex minimization variational inequality |
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