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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2015, Vol. 32 ›› Issue (1): 131-144.doi: 10.3969/j.issn.1005-3085.2015.01.013

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求解对称锥互补问题的一种非精确光滑牛顿方法(英)

芮绍平   

  1. 淮北师范大学数学科学学院，淮北  235000
  • 收稿日期:2013-10-06 接受日期:2014-01-07 出版日期:2015-02-15 发布日期:2015-04-15
  • 基金资助:
    安徽省教育厅自然科学基金 (KJ2013A235).

An Inexact Smoothing Newton Method for Solving Symmetric Cone Complementarity Problem

RUI Shao-ping   

  1. School of Mathematical Science, Huaibei Normal University, Huaibei 235000
  • Received:2013-10-06 Accepted:2014-01-07 Online:2015-02-15 Published:2015-04-15
  • Supported by:
    The Natural Science Foundation of Education Department of Anhui Province (KJ2013A235).

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摘要： 本文给出了一种求解对称锥互补问题的非精确光滑牛顿方法，所采用的互补函数是含一个参数且以FB和CHKS为特例的光滑函数．新方法的每步迭代中，都采用非精确牛顿方法求解由原问题产生的子问题．在一定条件下，新算法具有全局收敛和局部超线性收敛的性质．数值试验表明算法对于求解大规模对称锥互补问题是非常有效的．

关键词: 对称锥互补问题, 非精确牛顿法, 欧几里得若当代数, 大规模问题

Abstract:

In this paper, we propose an inexact smoothing method for solving symmetric cone complementarity problem based on a one-parametric class of smoothing function which contains the FB smoothing function and the CHKS smoothing function as special cases. At each iteration, we use the GMRES iterative solver to obtain an approximate solution to the generated smoothing Newton linear system. Under suitable conditions, we obtain global convergence and local superlinear convergence of the proposed algorithm. Numerical results indicate that the proposed algorithm is effective for large-scale problem.

Key words: symmetric cone complementarity problem, inexact smoothing algorithm, Euclidean Jordan algebra, large-scale problem

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