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Applied Mathematics and Mechanics (English Edition) ›› 2011, Vol. 32 ›› Issue (4): 521-532.doi: https://doi.org/10.1007/s10483-011-1435-x

• Articles • 上一篇    

Two new predictor-corrector algorithms for second-order cone programming

曾友芳1,2 白延琴1 简金宝2 唐春明2   

  1. 1. Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China;
    2. College of Mathematics and Information Science, Guangxi University, Nanning 530004, P. R. China
  • 收稿日期:2010-12-20 修回日期:2011-02-24 出版日期:2011-03-29 发布日期:2011-04-01

Two new predictor-corrector algorithms for second-order cone programming

 ZENG You-Fang1,2, BAI Yan-Qin1, JIAN Jin-Bao2, TANG Chun-Ming2   

  1. 1. Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China;
    2. College of Mathematics and Information Science, Guangxi University, Nanning 530004, P. R. China
  • Received:2010-12-20 Revised:2011-02-24 Online:2011-03-29 Published:2011-04-01

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865

被引次数

9

摘要： Based on the ideas of infeasible interior-point methods and predictor-corrector algorithms, two interior-point predictor-corrector algorithms for the second-order cone programming (SOCP) are presented. The two algorithms 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. These algorithms are suitable to the cases of feasible and infeasible interior iterative points. A simpler neighborhood of the central path for the SOCP is proposed, which is the pivotal difference from other interior-point predictor-corrector algorithms. Under some assumptions, the algorithms possess the global, linear, and quadratic convergence. The complexity bound O(rln(ε0/ε)) is obtained, where r denotes the number of the second-order cones in the SOCP problem. The numerical results show that the proposed algorithms are effective.

Abstract: Based on the ideas of infeasible interior-point methods and predictor-corrector algorithms, two interior-point predictor-corrector algorithms for the second-order cone programming (SOCP) are presented. The two algorithms 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. These algorithms are suitable to the cases of feasible and infeasible interior iterative points. A simpler neighborhood of the central path for the SOCP is proposed, which is the pivotal difference from other interior-point predictor-corrector algorithms. Under some assumptions, the algorithms possess the global, linear, and quadratic convergence. The complexity bound O(rln(ε0/ε)) is obtained, where r denotes the number of the second-order cones in the SOCP problem. The numerical results show that the proposed algorithms are effective.

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