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An inexact restoration strategy for the globalization of the sSQP method

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  • D. Fernández
  • E. Pilotta
  • G. Torres

Abstract

A globally convergent algorithm based on the stabilized sequential quadratic programming (sSQP) method is presented in order to solve optimization problems with equality constraints and bounds. This formulation has attractive features in the sense that constraint qualifications are not needed at all. In contrast with classic globalization strategies for Newton-like methods, we do not make use of merit functions. Our scheme is based on performing corrections on the solutions of the subproblems by using an inexact restoration procedure. The presented method is well defined and any accumulation point of the generated primal sequence is either a Karush-Kuhn-Tucker point or a stationary (maybe feasible) point of the problem of minimizing the infeasibility. Also, under suitable hypotheses, the sequence generated by the algorithm converges Q-linearly. Numerical experiments are given to confirm theoretical results. Copyright Springer Science+Business Media, LLC 2013

Suggested Citation

  • D. Fernández & E. Pilotta & G. Torres, 2013. "An inexact restoration strategy for the globalization of the sSQP method," Computational Optimization and Applications, Springer, vol. 54(3), pages 595-617, April.
    • Handle: RePEc:spr:coopap:v:54:y:2013:i:3:p:595-617
    DOI: 10.1007/s10589-012-9502-y
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    References listed on IDEAS

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    1. Andreas Fischer & Ana Friedlander, 2010. "A new line search inexact restoration approach for nonlinear programming," Computational Optimization and Applications, Springer, vol. 46(2), pages 333-346, June.
    2. Teemu Pennanen, 2002. "Local Convergence of the Proximal Point Algorithm and Multiplier Methods Without Monotonicity," Mathematics of Operations Research, INFORMS, vol. 27(1), pages 170-191, February.
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    Cited by:

    1. A. Izmailov & M. Solodov, 2015. "Critical Lagrange multipliers: what we currently know about them, how they spoil our lives, and what we can do about it," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(1), pages 1-26, April.
    2. A. F. Izmailov & E. I. Uskov, 2017. "Subspace-stabilized sequential quadratic programming," Computational Optimization and Applications, Springer, vol. 67(1), pages 129-154, May.
    3. A. F. Izmailov & M. V. Solodov, 2015. "Newton-Type Methods: A Broader View," Journal of Optimization Theory and Applications, Springer, vol. 164(2), pages 577-620, February.
    4. A. F. Izmailov & M. V. Solodov & E. I. Uskov, 2016. "Globalizing Stabilized Sequential Quadratic Programming Method by Smooth Primal-Dual Exact Penalty Function," Journal of Optimization Theory and Applications, Springer, vol. 169(1), pages 148-178, April.
    5. A. F. Izmailov & M. V. Solodov & E. I. Uskov, 2019. "A globally convergent Levenberg–Marquardt method for equality-constrained optimization," Computational Optimization and Applications, Springer, vol. 72(1), pages 215-239, January.
    6. A. Izmailov & M. Solodov & E. Uskov, 2015. "Combining stabilized SQP with the augmented Lagrangian algorithm," Computational Optimization and Applications, Springer, vol. 62(2), pages 405-429, November.
    7. 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.
    8. Daniel Robinson, 2015. "Comments on: Critical Lagrange multipliers: what we currently know about them, how they spoil our lives, and what we can do about it," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(1), pages 43-47, April.

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