Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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AN AFFINE SCALING INTERIOR ALGORITHM VIA CONJUGATE GRADIENT AND LANCZOS METHODS FOR BOUND-CONSTRAINED NONLINEAR OPTIMIZATION

  • Jia, Chunxia (Mathematics and Science College, Shanghai Normal University) ;
  • Zhu, Detong (Business College, Shanghai Normal University)
  • Received : 2010.03.20
  • Accepted : 2010.06.19
  • Published : 2011.01.30
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Abstract

In this paper, we construct a new approach of affine scaling interior algorithm using the affine scaling conjugate gradient and Lanczos methods for bound constrained nonlinear optimization. We get the iterative direction by solving quadratic model via affine scaling conjugate gradient and Lanczos methods. By using the line search backtracking technique, we will find an acceptable trial step length along this direction which makes the iterate point strictly feasible and the objective function nonmonotonically decreasing. Global convergence and local superlinear convergence rate of the proposed algorithm are established under some reasonable conditions. Finally, we present some numerical results to illustrate the effectiveness of the proposed algorithm.

Keywords

Acknowledgement

Supported by : Shanghai Normal University, Scienti?c Computing Key Laboratory of Shanghai Universities

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