运筹与管理 ›› 2018, Vol. 27 ›› Issue (8): 92-98.DOI: 10.12005/orms.2018.0186

• 理论分析与方法探讨 • 上一篇    下一篇

求解特征值互补问题的一类ABS算法

黄迪帅,韩海山   

  1. 内蒙古民族大学 数学学院,内蒙古 通辽 028043
  • 收稿日期:2017-01-05 出版日期:2018-08-25
  • 作者简介:黄迪帅,男,硕士;韩海山,男,博士,教授,硕士生导师。

An ABS Algorithm for Eigenvalue Complementarity Problem

HUANG Di-shuai, HAN Hai-shan   

  1. Department of Mathematics, Inner Mongolia University for Nationalities, 028043 Tongliao, China
  • Received:2017-01-05 Online:2018-08-25

摘要: ABS算法是20世纪80年代初,由Abaffy,Broyden和Spedicato完成的用于求解线性方程组的含有三个参量的投影算法,是一类有限次迭代直接法。目前,ABS算法不仅可以求解线性与非线性方程组,还可以求解线性规划和具有线性约束的非线性规划等问题。本文即是利用ABS算法求解特征值互补问题的一种尝试,构造了求解特征值互补问题的ABS算法,证明了求解特征值互补问题的ABS算法的收敛性。数值例子充分验证了求解特征值互补问题的ABS算法的有效性。

关键词: 特征值互补问题, 非线性ABS算法, NCP函数

Abstract: An ABS algorithm is a projection algorithm with three parameters for solving linear equations, constructed by Abaffy, Broyden and Spedicato in the early 1980s. It is a kind of finite iterative direct method. At present, the ABS algorithm can solve not only the linear and nonlinear equations, but the linear programming and nonlinear programming problems with linear constraints as well. This paper is an attempt to solve the eigenvalue complementarity problem by ABS algorithm. The ABS algorithm for solving the eigenvalue complementarity problem is constructed and the convergence of the algorithm is proved. Numerical examples are presented to indicate the effectiveness of the algorithm.

Key words: eigenvalue complementarity problem, nonlinear ABS algorithm, NCP function

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