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Volume 26, Issue 4
An Affine Scaling Interior Algorithm via Conjugate Gradient Path for Solving Bound-Constrained Nonlinear Systems

Chunxia Jia & Detong Zhu

J. Comp. Math., 26 (2008), pp. 578-597.

Published online: 2008-08

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  • Abstract

In this paper we propose an affine scaling interior algorithm via conjugate gradient path for solving nonlinear equality systems subject to bounds on variables. By employing the affine scaling conjugate gradient path search strategy, we obtain an iterative direction by solving the linearize model. By using the line search technique, we will find an acceptable trial step length along this direction which is strictly feasible and makes the objective function nonmonotonically decreasing. The global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions. Furthermore, the numerical results of the proposed algorithm indicate to be effective.

  • Keywords

Conjugate gradient path, Interior points, Affine scaling.

  • AMS Subject Headings

90C30, 65K05.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-26-578, author = {Chunxia Jia and Detong Zhu}, title = {An Affine Scaling Interior Algorithm via Conjugate Gradient Path for Solving Bound-Constrained Nonlinear Systems}, journal = {Journal of Computational Mathematics}, year = {2008}, volume = {26}, number = {4}, pages = {578--597}, abstract = {

In this paper we propose an affine scaling interior algorithm via conjugate gradient path for solving nonlinear equality systems subject to bounds on variables. By employing the affine scaling conjugate gradient path search strategy, we obtain an iterative direction by solving the linearize model. By using the line search technique, we will find an acceptable trial step length along this direction which is strictly feasible and makes the objective function nonmonotonically decreasing. The global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions. Furthermore, the numerical results of the proposed algorithm indicate to be effective.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8643.html} }
TY - JOUR T1 - An Affine Scaling Interior Algorithm via Conjugate Gradient Path for Solving Bound-Constrained Nonlinear Systems AU - Chunxia Jia & Detong Zhu JO - Journal of Computational Mathematics VL - 4 SP - 578 EP - 597 PY - 2008 DA - 2008/08 SN - 26 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8643.html KW - Conjugate gradient path, Interior points, Affine scaling. AB -

In this paper we propose an affine scaling interior algorithm via conjugate gradient path for solving nonlinear equality systems subject to bounds on variables. By employing the affine scaling conjugate gradient path search strategy, we obtain an iterative direction by solving the linearize model. By using the line search technique, we will find an acceptable trial step length along this direction which is strictly feasible and makes the objective function nonmonotonically decreasing. The global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions. Furthermore, the numerical results of the proposed algorithm indicate to be effective.

Chunxia Jia and Detong Zhu. (2008). An Affine Scaling Interior Algorithm via Conjugate Gradient Path for Solving Bound-Constrained Nonlinear Systems. Journal of Computational Mathematics. 26 (4). 578-597. doi:
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