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首页> 外文期刊>Applications of Mathematics >A GLOBALLY CONVERGENT NON-INTERIOR POINT ALGORITHM WITH FULL NEWTON STEP FOR SECOND-ORDER CONE PROGRAMMING
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A GLOBALLY CONVERGENT NON-INTERIOR POINT ALGORITHM WITH FULL NEWTON STEP FOR SECOND-ORDER CONE PROGRAMMING

机译：二阶锥规划的全牛顿步骤的全局收敛非内部点算法

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摘要

A non-interior point algorithm based on projection for second-order cone programming problems is proposed and analyzed. The main idea of the algorithm is that we cast the complementary equation in the primal-dual optimality conditions as a projection equation. By using this reformulation, we only need to solve a system of linear equations with the same coefficient matrix and compute two simple projections at each iteration, without performing any line search. This algorithm can start from an arbitrary point, and does not require the row vectors of A to be linearly independent. We prove that our algorithm is globally convergent under weak conditions. Preliminary numerical results demonstrate the effectiveness of our algorithm.
机译：提出并分析了一种基于投影的非内点算法求解二阶锥规划问题。该算法的主要思想是将原始对偶最优条件下的互补方程转换为投影方程。通过使用这种重构，我们只需要解决一个具有相同系数矩阵的线性方程组，并在每次迭代中计算两个简单的投影，而无需执行任何线搜索。该算法可以从任意点开始，并且不需要A的行向量是线性独立的。我们证明了我们的算法在弱条件下是全局收敛的。初步数值结果证明了该算法的有效性。

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  • 来源
    《Applications of Mathematics》 |2009年第5期|447-464|共18页
  • 作者

    Liang Fang; Guoping He; Li Sun;

  • 作者单位

    College of Mathematics and System Science, Taishan University, 271021 Tai'an, P.R.China and Department of Mathematics, Shanghai Jiao Tong University, 200240 Shanghai, P. R. China;

    College of Information Science and Engineering, Shandong University of Science and Technology, 266510 Qingdao, P. R. China, and Department of Mathematics, Shaghai Jiao Tong University, 200240 Shanghai, P.R.China;

    College of Information Science and Engineering, Shandong Agricultural University, 271018 Tai'an, P. R. China;

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  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    non-interior point algorithm; second-order cone programming; Jordan product; optimality condition; central path;

    机译：非内点算法;二阶锥编程;乔丹产品;最优条件中央路径;

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