Volume 28, Issue 1
A New Trust-Region Algorithm for Nonlinear Constrained Optimization

Lingfeng Niu & Yaxiang Yuan

J. Comp. Math., 28 (2010), pp. 72-86.

Published online: 2010-02

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  • Abstract

We propose a new trust region algorithm for nonlinear constrained optimization problems. In each iteration of our algorithm, the trial step is computed by minimizing a quadratic approximation to the augmented Lagrange function in the trust region. The augmented Lagrange function is also used as a merit function to decide whether the trial step should be accepted. Our method extends the traditional trust region approach by combining a filter technique into the rules for accepting trial steps so that a trial step could still be accepted even when it is rejected by the traditional rule based on merit function reduction. An estimate of the Lagrange multiplier is updated at each iteration, and the penalty parameter is updated to force sufficient reduction in the norm of the constraint violations. Active set technique is used to handle the inequality constraints. Numerical results for a set of constrained problems from the CUTEr collection are also reported.  

  • Keywords

Trust region method Augmented Lagrange function Filter method active set

  • AMS Subject Headings

90C30 65K05.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-28-72, author = {}, title = {A New Trust-Region Algorithm for Nonlinear Constrained Optimization}, journal = {Journal of Computational Mathematics}, year = {2010}, volume = {28}, number = {1}, pages = {72--86}, abstract = {

We propose a new trust region algorithm for nonlinear constrained optimization problems. In each iteration of our algorithm, the trial step is computed by minimizing a quadratic approximation to the augmented Lagrange function in the trust region. The augmented Lagrange function is also used as a merit function to decide whether the trial step should be accepted. Our method extends the traditional trust region approach by combining a filter technique into the rules for accepting trial steps so that a trial step could still be accepted even when it is rejected by the traditional rule based on merit function reduction. An estimate of the Lagrange multiplier is updated at each iteration, and the penalty parameter is updated to force sufficient reduction in the norm of the constraint violations. Active set technique is used to handle the inequality constraints. Numerical results for a set of constrained problems from the CUTEr collection are also reported.  

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2009.09-m2924}, url = {http://global-sci.org/intro/article_detail/jcm/8508.html} }
TY - JOUR T1 - A New Trust-Region Algorithm for Nonlinear Constrained Optimization JO - Journal of Computational Mathematics VL - 1 SP - 72 EP - 86 PY - 2010 DA - 2010/02 SN - 28 DO - http://doi.org/10.4208/jcm.2009.09-m2924 UR - https://global-sci.org/intro/article_detail/jcm/8508.html KW - Trust region method KW - Augmented Lagrange function KW - Filter method KW - active set AB -

We propose a new trust region algorithm for nonlinear constrained optimization problems. In each iteration of our algorithm, the trial step is computed by minimizing a quadratic approximation to the augmented Lagrange function in the trust region. The augmented Lagrange function is also used as a merit function to decide whether the trial step should be accepted. Our method extends the traditional trust region approach by combining a filter technique into the rules for accepting trial steps so that a trial step could still be accepted even when it is rejected by the traditional rule based on merit function reduction. An estimate of the Lagrange multiplier is updated at each iteration, and the penalty parameter is updated to force sufficient reduction in the norm of the constraint violations. Active set technique is used to handle the inequality constraints. Numerical results for a set of constrained problems from the CUTEr collection are also reported.  

Lingfeng Niu & Yaxiang Yuan. (2019). A New Trust-Region Algorithm for Nonlinear Constrained Optimization. Journal of Computational Mathematics. 28 (1). 72-86. doi:10.4208/jcm.2009.09-m2924
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