| 一个求解二阶锥规划的光滑牛顿算法 |
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| 引用本文： | 董丽,王洪芹,潘虹.一个求解二阶锥规划的光滑牛顿算法[J].数学杂志,2015,35(6):1453-1460. |
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| 作者姓名： | 董丽 王洪芹 潘虹 |
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| 作者单位： | 信阳师范学院数学与信息科学学院, 河南 信阳 464000,中国农业大学烟台研究院, 山东 烟台 264670,信阳师范学院数学与信息科学学院, 河南 信阳 464000 |
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| 基金项目： | 河南省基础与前沿技术研究计划项目(142300410318);河南省教育厅科学技术研究重点项目(13A110767). |
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| 摘 要： | 本文研究了二阶锥规划问题.利用新的最小值函数的光滑函数,给出一个求解二阶锥规划的光滑牛顿算法.算法可以从任意点出发,在每一步迭代只需求解一个线性方程组并进行一次线性搜索.在不需要满足严格互补假设条件下,证明了算法是全局收敛和局部二阶收敛的.数值试验表明算法是有效的.
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| 关 键 词： | 二阶锥规划 光滑牛顿算法 收敛性 |
| 收稿时间： | 2013/12/11 0:00:00 |
| 修稿时间： | 2014/5/15 0:00:00 |
A SMOOTHING NEWTON METHOD FOR SOLVING THE SECOND-ORDER CONE PROGRAMMING |
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| DONG Li,WANG Hong-qin and PAN Hong.A SMOOTHING NEWTON METHOD FOR SOLVING THE SECOND-ORDER CONE PROGRAMMING[J].Journal of Mathematics,2015,35(6):1453-1460. |
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| Authors: | DONG Li WANG Hong-qin and PAN Hong |
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| Institution: | College of Math. and Information Science, Xinyang Normal University, Xinyang 464000, China,School of Technology, Yantai Research Institute of China Agricultural University, Yantai 264670, China and College of Math. and Information Science, Xinyang Normal University, Xinyang 464000, China |
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| Abstract: | In this paper, we study the the second-order cone programming. By using a new smoothing function of the vector minimum function, a smoothing Newton method is proposed to solve the second-order cone programming. The proposed algorithm can start from arbitrary initial point. It solves only one system of linear equations and performs only one line search. We prove the global and local quadratical convergence of the proposed algorithm in absence of strict complementarity. Numerical experiments demonstrate the efficiency of our algorithm. |
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| Keywords: | second-order cone programming smoothing Newton method convergence |
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