| 二阶锥规划两个新的预估-校正算法 |
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| 引用本文： | 曾友芳,白延琴,简金宝,唐春明. 二阶锥规划两个新的预估-校正算法[J]. 应用数学和力学, 2011, 32(4): 497-508. DOI: 10.3879/j.issn.1000-0887.2011.04.012 |
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| 作者姓名： | 曾友芳 白延琴 简金宝 唐春明 |
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| 作者单位： | 上海大学 数学系, 上海 200444; |
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| 基金项目： | 国家自然科学基金资助项目(71061002;11071158); 广西自然科学基金资助项目(0832052;2010GXNSFB013047) |
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| 摘 要： | 基于不可行内点法和预估-校正算法的思想,提出两个新的求解二阶锥规划的内点预估-校正算法．其预估方向分别是Newton方向和Euler方向,校正方向属于Alizadeh-Haeberly-Overton(AHO)方向的范畴．算法对于迭代点可行或不可行的情形都适用．主要构造了一个更简单的中心路径的邻域,这是有别于其它内点预估-校正算法的关键．在一些假设条件下,算法具有全局收敛性、线性和二次收敛速度,并获得了O(rln(ε0/ε))的迭代复杂性界,其中r表示二阶锥规划问题所包含的二阶锥约束的个数．数值实验结果表明提出的两个算法是有效的．
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| 关 键 词： | 二阶锥规划 不可行内点算法 预估-校正算法 全局收敛性 复杂性分析 |
| 收稿时间： | 2010-12-30 |
Two New Predictor-Corrector Algorithms for Second-Order Cone Programming |
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| ZENG You-fang,BAI Yan-qin,JIAN Jin-bao,TANG Chun-ming. Two New Predictor-Corrector Algorithms for Second-Order Cone Programming[J]. Applied Mathematics and Mechanics, 2011, 32(4): 497-508. DOI: 10.3879/j.issn.1000-0887.2011.04.012 |
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| Authors: | ZENG You-fang BAI Yan-qin JIAN Jin-bao TANG Chun-ming |
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| Affiliation: | Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China;College of Mathematics and Information Science, Guangxi University, Nanning 530004, P. R. China |
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| Abstract: | Based on the ideas of infeasible interior-point methods and predictor-corrector algorithms,two interior-point predictor-corrector algorithms for second-order cone programming(SOCP) were presented.They use the Newton direction and the Euler direction as the predictor directions,respectively.The corrector directions belong to the category of the Alizadeh-Haeberly-Overton(AHO) directions.The two new algorithms were suitable to cases of feasible and infeasible interior iterative points.A simpler neighborhood of... |
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| Keywords: | second-order cone programming infeasible interior-point algorithm predictor-corrector algorithm global convergence complexity analysis |
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