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An alternating structured trust region algorithm for separable optimization problems with nonconvex constraints

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  • Dan Xue

  • Wenyu Sun

  • Liqun Qi

Abstract

In this paper, we propose a structured trust-region algorithm combining with filter technique to minimize the sum of two general functions with general constraints. Specifically, the new iterates are generated in the Gauss-Seidel type iterative procedure, whose sizes are controlled by a trust-region type parameter. The entries in the filter are a pair: one resulting from feasibility; the other resulting from optimality. The global convergence of the proposed algorithm is proved under some suitable assumptions. Some preliminary numerical results show that our algorithm is potentially efficient for solving general nonconvex optimization problems with separable structure. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Dan Xue & Wenyu Sun & Liqun Qi, 2014. "An alternating structured trust region algorithm for separable optimization problems with nonconvex constraints," Computational Optimization and Applications, Springer, vol. 57(2), pages 365-386, March.
    • Handle: RePEc:spr:coopap:v:57:y:2014:i:2:p:365-386
    DOI: 10.1007/s10589-013-9597-9
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    References listed on IDEAS

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    1. Yan Zhang & Wenyu Sun & Liqun Qi, 2010. "A Nonmonotone Filter Barzilai-Borwein Method For Optimization," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 27(01), pages 55-69.
    2. Wenyu Sun & Ya-Xiang Yuan, 2006. "Optimization Theory and Methods," Springer Optimization and Its Applications, Springer, number 978-0-387-24976-6, March.
    3. Yan Chen & Robert Gazzale, 2004. "When Does Learning in Games Generate Convergence to Nash Equilibria? The Role of Supermodularity in an Experimental Setting," American Economic Review, American Economic Association, vol. 94(5), pages 1505-1535, December.
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    Cited by:

    1. X. Wang & S. Li & X. Kou & Q. Zhang, 2015. "A new alternating direction method for linearly constrained nonconvex optimization problems," Journal of Global Optimization, Springer, vol. 62(4), pages 695-709, August.
    2. Jean-Hubert Hours & Colin N. Jones, 2017. "An Alternating Trust Region Algorithm for Distributed Linearly Constrained Nonlinear Programs, Application to the Optimal Power Flow Problem," Journal of Optimization Theory and Applications, Springer, vol. 173(3), pages 844-877, June.

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