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A stabilized filter SQP algorithm for nonlinear programming

Author

Listed:
  • Chungen Shen

    (University of Shanghai for Science and Technology)

  • Lei-Hong Zhang

    (Shanghai University of Finance and Economics
    Shanghai Key Laboratory of Financial Information Technology (Shanghai University of Finance and Economics))

  • Wei Liu

    (Shanghai Key Laboratory of Financial Information Technology (Shanghai University of Finance and Economics)
    Shanghai Finance University)

Abstract

This paper presents a stabilized filter sequential quadratic programming (SQP) method for the general nonlinear optimization problems. The technique of stabilizing the inner quadratic programmings is an efficient strategy for the degenerate problem and brings the local superlinear convergence, while the integrated filter technique works effectively and guarantees the global convergence. The new algorithm works on both the primal and dual variables and solves the problem within the computational complexity comparable to the classical SQP algorithm. For the convergence, we show that (1) it converges either to a Karush–Kuhn–Tucker point at which the cone-continuity property holds, or to a stationary point in the sense of minimizing the constraint violation, and (2) under some second-order sufficient conditions, it converges locally superlinearly without any constraint qualifications. Our preliminary numerical results on a set of CUTEr test problems as well as on degenerate problems demonstrate the efficiency of the new algorithm.

Suggested Citation

  • Chungen Shen & Lei-Hong Zhang & Wei Liu, 2016. "A stabilized filter SQP algorithm for nonlinear programming," Journal of Global Optimization, Springer, vol. 65(4), pages 677-708, August.
    • Handle: RePEc:spr:jglopt:v:65:y:2016:i:4:d:10.1007_s10898-015-0400-6
    DOI: 10.1007/s10898-015-0400-6
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    References listed on IDEAS

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    1. Chungen Shen & Sven Leyffer & Roger Fletcher, 2012. "A nonmonotone filter method for nonlinear optimization," Computational Optimization and Applications, Springer, vol. 52(3), pages 583-607, July.
    2. R. Andreani & J. M. Martinez & M. L. Schuverdt, 2005. "On the Relation between Constant Positive Linear Dependence Condition and Quasinormality Constraint Qualification," Journal of Optimization Theory and Applications, Springer, vol. 125(2), pages 473-483, May.
    3. Andreas Fischer, 1999. "Modified Wilson's Method for Nonlinear Programs with Nonunique Multipliers," Mathematics of Operations Research, INFORMS, vol. 24(3), pages 699-727, August.
    4. A. Izmailov & A. Kurennoy & M. Solodov, 2015. "Local convergence of the method of multipliers for variational and optimization problems under the noncriticality assumption," Computational Optimization and Applications, Springer, vol. 60(1), pages 111-140, January.
    5. Zsolt Ugray & Leon Lasdon & John Plummer & Fred Glover & James Kelly & Rafael Martí, 2007. "Scatter Search and Local NLP Solvers: A Multistart Framework for Global Optimization," INFORMS Journal on Computing, INFORMS, vol. 19(3), pages 328-340, August.
    6. Daniel Ralph & Stephen J. Wright, 2000. "Superlinear Convergence of an Interior-Point Method Despite Dependent Constraints," Mathematics of Operations Research, INFORMS, vol. 25(2), pages 179-194, May.
    7. Joseph Frédéric Bonnans & Alexander Ioffe, 1995. "Second-order Sufficiency and Quadratic Growth for Nonisolated Minima," Mathematics of Operations Research, INFORMS, vol. 20(4), pages 801-817, November.
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    Cited by:

    1. Renke Kuhlmann & Christof Büskens, 2018. "A primal–dual augmented Lagrangian penalty-interior-point filter line search algorithm," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(3), pages 451-483, June.
    2. Songqiang Qiu, 2019. "Convergence of a stabilized SQP method for equality constrained optimization," Computational Optimization and Applications, Springer, vol. 73(3), pages 957-996, July.

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