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A subspace SQP method for equality constrained optimization

Author

Listed:
  • Jae Hwa Lee

    (Sungkyunkwan University)

  • Yoon Mo Jung

    (Sungkyunkwan University)

  • Ya-xiang Yuan

    (ICMSEC, AMSS, CAS)

  • Sangwoon Yun

    (Sungkyunkwan University)

Abstract

In this paper, we present a subspace method for solving large scale nonlinear equality constrained optimization problems. The proposed method is based on a SQP method combined with the limited-memory BFGS update formula. Each subproblem is solved in a theoretically suitable subspace. In the case of few constraints, we show that our search direction in the subspace is equivalent to that of the SQP subproblem in the full space. In the case of many constraints, we reduce the number of constraints in the subproblem and we show that the solution of the subspace subproblem is a descent direction of a particular exact penalty function. Global convergence properties of the proposed method are given for both cases. Numerical results are given to illustrate the soundness of the proposed model.

Suggested Citation

  • Jae Hwa Lee & Yoon Mo Jung & Ya-xiang Yuan & Sangwoon Yun, 2019. "A subspace SQP method for equality constrained optimization," Computational Optimization and Applications, Springer, vol. 74(1), pages 177-194, September.
    • Handle: RePEc:spr:coopap:v:74:y:2019:i:1:d:10.1007_s10589-019-00109-6
    DOI: 10.1007/s10589-019-00109-6
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    References listed on IDEAS

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    1. Nicholas Gould & Dominique Orban & Philippe Toint, 2015. "CUTEst: a Constrained and Unconstrained Testing Environment with safe threads for mathematical optimization," Computational Optimization and Applications, Springer, vol. 60(3), pages 545-557, April.
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