A Nonmonotone Trust Region Method for Nonlinear Programming with Simple Bound Constraints

doi:10.1007/S002450010020

Title: A Nonmonotone Trust Region Method for Nonlinear Programming with Simple Bound Constraints

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Abstract

In this paper we propose a nonmonotone trust region algorithm for optimization with simple bound constraints. Under mild conditions, we prove the global convergence of the algorithm. For the monotone case it is also proved that the correct active set can be identified in a finite number of iterations if the strict complementarity slackness condition holds, and so the proposed algorithm reduces finally to an unconstrained minimization method in a finite number of iterations, allowing a fast asymptotic rate of convergence. Numerical experiments show that the method is efficient.

Authors:

Chen, Z.-W. ^[1]; Han, J.-Y. ^[2]; Xu, D.-C. ^[3]

Department of Mathematics, Suzhou University, Suzhou 215006, Jiangsu Province (China), E-mail: wenchen@pub.sz.jsinfo.net
Institute of Applied Mathematics, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100080 (China), E-mail: hjyyyf@netease.com
Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100080 (China), E-mail: xudc@lsec.cc.ac.cn

Publication Date:: Sun Jul 01 00:00:00 EDT 2001

OSTI Identifier:: 21067512

Resource Type:: Journal Article

Journal Name:: Applied Mathematics and Optimization

Additional Journal Information:: Journal Volume: 43; Journal Issue: 1; Other Information: DOI: 10.1007/s002450010020; Copyright (c) Inc. 2000 Springer-Verlag New York; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0095-4616

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; ASYMPTOTIC SOLUTIONS; CONVERGENCE; MINIMIZATION; NONLINEAR PROGRAMMING

Citation Formats


                    Chen, Z.-W., Han, J.-Y., and Xu, D.-C. A Nonmonotone Trust Region Method for Nonlinear Programming with Simple Bound Constraints.  United States: N. p., 2001. 
        Web.  doi:10.1007/S002450010020.

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                    Chen, Z.-W., Han, J.-Y., & Xu, D.-C. A Nonmonotone Trust Region Method for Nonlinear Programming with Simple Bound Constraints.  United States.  https://doi.org/10.1007/S002450010020

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                    Chen, Z.-W., Han, J.-Y., and Xu, D.-C. 2001.  
        "A Nonmonotone Trust Region Method for Nonlinear Programming with Simple Bound Constraints".  United States.  https://doi.org/10.1007/S002450010020.

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@article{osti_21067512,

  title        = {A Nonmonotone Trust Region Method for Nonlinear Programming with Simple Bound Constraints},

  author       = {Chen, Z.-W. and Han, J.-Y. and Xu, D.-C.},

  abstractNote = {In this paper we propose a nonmonotone trust region algorithm for optimization with simple bound constraints. Under mild conditions, we prove the global convergence of the algorithm. For the monotone case it is also proved that the correct active set can be identified in a finite number of iterations if the strict complementarity slackness condition holds, and so the proposed algorithm reduces finally to an unconstrained minimization method in a finite number of iterations, allowing a fast asymptotic rate of convergence. Numerical experiments show that the method is efficient.},

  doi          = {10.1007/S002450010020},

  url          = {https://www.osti.gov/biblio/21067512},
  journal      = {Applied Mathematics and Optimization},

  issn         = {0095-4616},

  number       = 1,

  volume       = 43,

  place        = {United States},

  year         = {Sun Jul 01 00:00:00 EDT 2001},

  month        = {Sun Jul 01 00:00:00 EDT 2001}

}

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