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http://dx.doi.org/10.14317/jami.2011.29.1_2.173

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)
Publication Information
Journal of applied mathematics & informatics / v.29, no.1_2, 2011 , pp. 173-190 More about this Journal
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
Lanczos method; Conjugate gradient; Interior points; Affine scaling;
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