| 一种求解半定规划的邻近外梯度算法 |
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| 引用本文： | 于冬梅,高雷阜,赵世杰,杨培. 一种求解半定规划的邻近外梯度算法[J]. 数学杂志, 2016, 36(5): 1047-1055 |
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| 作者姓名： | 于冬梅 高雷阜 赵世杰 杨培 |
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| 作者单位： | 辽宁工程技术大学优化与决策研究所, 辽宁 阜新 123000,辽宁工程技术大学优化与决策研究所, 辽宁 阜新 123000,辽宁工程技术大学优化与决策研究所, 辽宁 阜新 123000,辽宁工程技术大学优化与决策研究所, 辽宁 阜新 123000 |
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| 基金项目： | 教育部高校博士学科科研基金联合资助项目(20132121110009);国家自然科学基金天元基金(11326224);辽宁省教育厅基金资助项目(L2012105). |
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| 摘 要： | 本文提出了一种求解半定规划的邻近外梯度算法.通过转化半定规划的最优性条件为变分不等式,在变分不等式满足单调性和Lipschitz连续的前提下,构造包含原投影区域的半空间,产生邻近点序列来逼近变分不等式的解,简化了投影的求解过程.将该算法应用到教育测评问题中,数值实验结果表明,该方法是解大规模半定规划问题的一种可行方法.
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| 关 键 词： | 半定规划 变分不等式 次梯度半空间 外梯度算法 |
| 收稿时间： | 2014-04-02 |
| 修稿时间： | 2014-07-02 |
A PROXIMAL EXTRAGRADIENT ALGORITHM FOR SEMIDEFINITE PROGRAMMING |
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| YU Dong-mei,GAO Lei-fu,ZHAO Shi-jie and YANG Pei. A PROXIMAL EXTRAGRADIENT ALGORITHM FOR SEMIDEFINITE PROGRAMMING[J]. Journal of Mathematics, 2016, 36(5): 1047-1055 |
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| Authors: | YU Dong-mei GAO Lei-fu ZHAO Shi-jie YANG Pei |
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| Affiliation: | Research Institute of Optim. and Decision, Liaoning Technical University, Fuxin 123000, China,Research Institute of Optim. and Decision, Liaoning Technical University, Fuxin 123000, China,Research Institute of Optim. and Decision, Liaoning Technical University, Fuxin 123000, China and Research Institute of Optim. and Decision, Liaoning Technical University, Fuxin 123000, China |
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| Abstract: | In this paper, we present a proximal extragradient algorithm for solving semidefinite programming probem. The optimality conditions for semidefinite programming are transformed into variational inequality problem. Under the premise of variational inequality monotone and Lipschitz continuous, half-space contains the original projection area is constructed, generated points sequence is approaching the solution of variational inequalities, such that the projection of the solution process is simplified. The algorithm is applied to educational evaluation questions, and numerical results show that the proposed method is feasible for solving large-scale semidefinite programming problem. |
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| Keywords: | semidefinite programming(SDP) variational inequalities subgradient half space extragradient algorithm |
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