| 一个新的求解二阶锥规划的非内部连续化算法 |
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| 引用本文： | 汤京永,贺国平.一个新的求解二阶锥规划的非内部连续化算法[J].应用数学,2012,25(1):26-31. |
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| 作者姓名： | 汤京永 贺国平 |
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| 作者单位： | 1. 信阳师范学院数学与信息科学学院,河南信阳464000;上海交通大学数学系,上海200240
2. 山东科技大学信息科学与工程学院,山东青岛,266510 |
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| 基金项目： | 国家自然科学基金，山东省自然科学基金，高等学校博士学科点专项科研基金 |
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| 摘 要： | 基于光滑Fischer-Burmeister函数,本文给出一个新的求解二阶锥规划的非内部连续化算法.算法对初始点的选取没有任何限制,并且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条件下,证明了算法是全局收敛且是局部超线性收敛的.数值试验表明算法是有效的.
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| 关 键 词： | 二阶锥规划 非内部连续化算法 光滑函数 全局收敛 超线性收敛 |
A New Non-interior Continuation Method for Second-order Cone Programming |
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| TANG Jingyong
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HE Guoping.A New Non-interior Continuation Method for Second-order Cone Programming[J].Mathematica Applicata,2012,25(1):26-31. |
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| Authors: | TANG Jingyong HE Guoping |
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| Institution: | 1.College of Mathematics and Information Science,Xinyang Normal University,Xinyang 464000,China;2.Department of Mathematics,Shanghai Jiaotong University,Shanghai 200240,China;3.College of Information Science and Engineering,Shandong University of Science and Technology,Qingdao 266510,China) |
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| Abstract: | Based on the Fischer-Burmeister smoothing function,a new non-interior continuation method is presented for solving the second-order cone programming.The proposed algorithm does not have restrictions regarding its starting point,and solves only one linear system of equations and performs only one line search at each iteration.Without requiring strict complementarity assumption,the proposed algorithm is proved to be globally and locally superlinearly convergent under suitable assumptions.Numerical results indicate that our algorithm is efficient in practical computation. |
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| Keywords: | Second-order cone programming Non-interior continuation method Smoothing function Global convergence Superlinear convergence |
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