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A globally and quadratically convergent smoothing Newton method for solving second-order cone optimization

机译：求解二次锥优化的全局和二次收敛平滑牛顿法

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摘要

Second-order cone optimization (denoted by SOCO) is a class of convex optimization problems and it contains the linear optimization problem, convex quadratic optimization problem and quadratically constrained convex quadratic optimization problem as special cases. In this paper, we propose a new smoothing Newton method for solving the SOCO based on a non-symmetrically perturbed smoothing Fischer-Burmeister function. At each iteration, a system of linear equations is solved only approximately by using the inexact Newton method. It is shown that any accumulation point of the iteration sequence generated by the proposed algorithm is a solution of the SOCO. Furthermore, we prove that the generated sequence is bounded and hence it has at least one accumulation point. Under the assumption of nonsingularity, we establish the local quadratic convergence of the proposed algorithm without strict complementarity condition. Numerical experiments indicate that our method is effective.
机译：二阶锥优化（用SOCO表示）是一类凸优化问题，其中包含线性优化问题，凸二次优化问题和二次约束凸二次优化问题。在本文中，我们提出了一种基于非对称扰动平滑Fischer-Burmeister函数的新的牛顿平滑法。在每次迭代中，使用不精确的牛顿法只能近似求解线性方程组。结果表明，所提算法生成的迭代序列的任何累加点都是SOCO的解。此外，我们证明生成的序列是有界的，因此它至少具有一个累积点。在非奇异性的假设下，我们建立了该算法的局部二次收敛性，没有严格的互补条件。数值实验表明，该方法是有效的。

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  • 来源
    《Applied Mathematical Modelling》 |2015年第8期|2180-2193|共14页
  • 作者

    Jingyong Tang; Guoping He; Li Dong; Liang Fang; Jinchuan Zhou;

  • 作者单位

    College of Mathematics and Information Science, Xinyang Normal University, Xinyang 464000, China,Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China;

    College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao 266510, China;

    College of Mathematics and Information Science, Xinyang Normal University, Xinyang 464000, China;

    College of Mathematics and System Science, Taishan University, Tai'an 271021, China;

    Department of Mathematics, School of Science, Shandong University of Technology, Zibo 255049, China;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Second-order cone optimization; Smoothing Newton method; Global convergence; Quadratic convergence;

    机译：二阶锥优化;平滑牛顿法;全球趋同;二次收敛;

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