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均衡及约束凸优化问题公共解的一般迭代算法

A general iterative algorithm for finding a common solution of equilibrium and constrained convex minimization problems
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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. 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.
作者 田明 刘磊
机构地区 中国民航大学理学院
出处 《中国科学：数学》 CSCD 北大核心 2013年第4期365-381,共17页 Scientia Sinica：Mathematica
基金 中央高校基本科研业务费专项资金(批准号:ZXH2012K001) 中国民航大学应用基础研究(批准号:2012KYM03)资助项目
关键词 均衡问题 约束凸优化问题 变分不等式 equilibrium problem constrained convex minimization variational inequality
分类号 O224 [理学—运筹学与控制论]
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中国科学：数学
2013年 第4期

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