| 均衡问题的一种改进不精确次梯度算法 |
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| 引用本文： | 党亚峥,沈忱,刘雯雯.均衡问题的一种改进不精确次梯度算法[J].上海理工大学学报,2016,38(6):523-526,534. |
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| 作者姓名： | 党亚峥 沈忱 刘雯雯 |
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| 作者单位： | 上海理工大学 管理学院, 上海 200093,上海理工大学 管理学院, 上海 200093,上海理工大学 管理学院, 上海 200093 |
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| 基金项目： | 上海市自然科学基金资助项目（14ZR1429200）；上海市教育委员会科研创新项目（15ZZ073） |
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| 摘 要： | 针对采用精确次梯度算法求解均衡问题中的稳固非扩张算子的不动点集问题(EP(f,Fix(T)))时计算复杂且收敛性较差这一情况,提出了一种改进的不精确次梯度算法.首先,由事先选择的参数确定一个凸集;其次,通过不精确次梯度投影算法构造中间迭代点;最后,将当前迭代点和中间迭代点的线性组合在稳固非扩张算子的映射作为下一次迭代点.在合适条件下验证了算法的全局收敛性.
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| 关 键 词： | 均衡问题 次梯度 稳固非扩张映射 全局收敛 |
| 收稿时间： | 2016/4/1 0:00:00 |
Improved Subgradient Algorithm for Equalization Problems |
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| DANG Yazheng,SHEN Chen and LIU Wengweng.Improved Subgradient Algorithm for Equalization Problems[J].Journal of University of Shanghai For Science and Technology,2016,38(6):523-526,534. |
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| Authors: | DANG Yazheng SHEN Chen and LIU Wengweng |
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| Institution: | Business School, University of Shanghai for Science and Technology, Shanghai 200093, China,Business School, University of Shanghai for Science and Technology, Shanghai 200093, China and Business School, University of Shanghai for Science and Technology, Shanghai 200093, China |
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| Abstract: | The exact subgradient algorithm for solving the equilibrium problem (EP(f,Fix(T))) of sets over the fixed point of non-expansive operator causes computational complexity and poor convergence.To overcome the defect,an inexact subgradient algorithm for the EP(f,Fix(T)) was presented.A convex set assured by given parameter was selected,the intermediate iterative point was constructed by using the non-accurate subgradient projection algorithm and the image,under firmly non-expansive operator of the linear combination of the current iterative point and middle iterative point was taken as the next iteration point.Under suitable conditions,the global convergence of the algorithm was verified. |
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| Keywords: | equilibrium problem sub-gradient firmly non-expansive mapping global convergence |
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