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Volume 30, Issue 3
A New Trust-Region Algorithm for Finite Minimax Problem

Fusheng Wang, Chuanlong Wang & Li Wang

DOI: 10.4208/jcm.1109-m3567

J. Comp. Math., 30 (2012), pp. 262-278.

Published online: 2012-06

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  • Abstract

In this paper, a new trust region algorithm for minimax optimization problems is proposed, which solves only one quadratic subproblem based on a new approximation model at each iteration. The approach is different from the traditional algorithms that usually require to solve two quadratic subproblems. Moreover, to avoid Maratos effect, the nonmonotone strategy is employed. The analysis shows that, under standard conditions, the algorithm has global and superlinear convergence. Preliminary numerical experiments are conducted to show the efficiency of the new method.

  • Keywords

Trust-region methods, Minimax optimization, Nonmonotone strategy, Global convergence, Superlinear convergence.

  • AMS Subject Headings

90C47, 49K35.

  • Copyright

COPYRIGHT: © Global Science Press

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  • BibTex
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  • TXT
@Article{JCM-30-262, author = {Wang , FushengWang , Chuanlong and Wang , Li}, title = {A New Trust-Region Algorithm for Finite Minimax Problem}, journal = {Journal of Computational Mathematics}, year = {2012}, volume = {30}, number = {3}, pages = {262--278}, abstract = {

In this paper, a new trust region algorithm for minimax optimization problems is proposed, which solves only one quadratic subproblem based on a new approximation model at each iteration. The approach is different from the traditional algorithms that usually require to solve two quadratic subproblems. Moreover, to avoid Maratos effect, the nonmonotone strategy is employed. The analysis shows that, under standard conditions, the algorithm has global and superlinear convergence. Preliminary numerical experiments are conducted to show the efficiency of the new method.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1109-m3567}, url = {http://global-sci.org/intro/article_detail/jcm/8429.html} }
TY - JOUR T1 - A New Trust-Region Algorithm for Finite Minimax Problem AU - Wang , Fusheng AU - Wang , Chuanlong AU - Wang , Li JO - Journal of Computational Mathematics VL - 3 SP - 262 EP - 278 PY - 2012 DA - 2012/06 SN - 30 DO - http://doi.org/10.4208/jcm.1109-m3567 UR - https://global-sci.org/intro/article_detail/jcm/8429.html KW - Trust-region methods, Minimax optimization, Nonmonotone strategy, Global convergence, Superlinear convergence. AB -

In this paper, a new trust region algorithm for minimax optimization problems is proposed, which solves only one quadratic subproblem based on a new approximation model at each iteration. The approach is different from the traditional algorithms that usually require to solve two quadratic subproblems. Moreover, to avoid Maratos effect, the nonmonotone strategy is employed. The analysis shows that, under standard conditions, the algorithm has global and superlinear convergence. Preliminary numerical experiments are conducted to show the efficiency of the new method.

Wang , FushengWang , Chuanlong and Wang , Li. (2012). A New Trust-Region Algorithm for Finite Minimax Problem. Journal of Computational Mathematics. 30 (3). 262-278. doi:10.4208/jcm.1109-m3567
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