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| An O（rL） Infeasible Interior-point Algorithm for Symmetric Cone LCP via CHKS Function | |
| 引用本文： | Zi-yan Luo,Nai-hua Xiu. An O（rL） Infeasible Interior-point Algorithm for Symmetric Cone LCP via CHKS Function[J]. 应用数学学报(英文版), 2009, 25(4): 593-606. DOI: 10.1007/s10255-008-8814-2 |
| 作者姓名： | Zi-yan Luo Nai-hua Xiu |
| 作者单位： | [1]Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing 100044, China [2]Department of Mathematics, School of Science, Beijing Jiaotong University; Key Laboratory of Communication and Information System （Beijing Jiaotong University）, Beijing Municipal Commission of Education, Beijing 100044, China |
| 基金项目： | Supported by the National Natural Science Foundation of China （No. 10671010） and Specialized Research Fund for the Doctoral Program of Higher Education （200800040024）. |
| 摘 要： | In this paper, we propose a theoretical framework of an infeasible interior-point algorithm for solving monotone linear cornplementarity problems over symmetric cones （SCLCP）. The new algorithm gets Newton-like directions from the Chen-Harker-Kanzow-Smale （CHKS） smoothing equation of the SCLCP. It possesses the following features： The starting point is easily chosen; one approximate Newton step is computed and accepted at each iteration; the iterative point with unit stepsize automatically remains in the neighborhood of central path; the iterative sequence is bounded and possesses （9（rL） polynomial-time complexity under the monotonicity and solvability of the SCLCP. |
| 关 键 词： | 运算法则 相称性 LCP CHKS 数学分析 |
An $$mathcal{O}$$( rL) infeasible interior-point algorithm for symmetric cone LCP via CHKS function |
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| Zi-yan?LuoEmail author,Nai-hua?Xiu. An $$mathcal{O}$$( rL) infeasible interior-point algorithm for symmetric cone LCP via CHKS function[J]. Acta Mathematicae Applicatae Sinica, 2009, 25(4): 593-606. DOI: 10.1007/s10255-008-8814-2 | |
| Authors: | Zi-yan?Luo mailto:starkeynature@hotmail.com" title=" starkeynature@hotmail.com" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author,Nai-hua?Xiu |
| Affiliation: | 1.Department of Mathematics, School of Science,Beijing Jiaotong University,Beijing,China;2.Key Laboratory of Communication and Information System (Beijing Jiaotong University),Beijing Municipal Commission of Education,Beijing,China |
| Abstract: | In this paper, we propose a theoretical framework of an infeasible interior-point algorithm for solving monotone linear complementarity problems over symmetric cones (SCLCP). The new algorithm gets Newton-like directions from the Chen-Harker-Kanzow-Smale (CHKS) smoothing equation of the SCLCP. It possesses the following features: The starting point is easily chosen; one approximate Newton step is computed and accepted at each iteration; the iterative point with unit stepsize automatically remains in the neighborhood of central path; the iterative sequence is bounded and possesses $mathcal{O}$mathcal{O}(rL) polynomial-time complexity under the monotonicity and solvability of the SCLCP. |
| Keywords: | Infeasible interior-point algorithm symmetric cone linear complementarity problem monotonicity polynomial complexity |
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