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A Flexible Inexact-Restoration Method for Constrained Optimization

Author

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  • L. F. Bueno

    (Federal University of São Paulo)

  • G. Haeser

    (University of São Paulo)

  • J. M. Martínez

    (University of Campinas)

Abstract

We introduce a new flexible inexact-restoration algorithm for constrained optimization problems. In inexact-restoration methods, each iteration has two phases. The first phase aims at improving feasibility and the second phase aims to minimize a suitable objective function. In the second phase, we also impose bounded deterioration of the feasibility, obtained in the first phase. Here, we combine the basic ideas of the Fischer-Friedlander approach for inexact-restoration with the use of approximations of the Lagrange multipliers. We present a new option to obtain a range of search directions in the optimization phase, and we employ the sharp Lagrangian as merit function. Furthermore, we introduce a flexible way to handle sufficient decrease requirements and an efficient way to deal with the penalty parameter. Global convergence of the new inexact-restoration method to KKT points is proved under weak constraint qualifications.

Suggested Citation

  • L. F. Bueno & G. Haeser & J. M. Martínez, 2015. "A Flexible Inexact-Restoration Method for Constrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 165(1), pages 188-208, April.
    • Handle: RePEc:spr:joptap:v:165:y:2015:i:1:d:10.1007_s10957-014-0572-0
    DOI: 10.1007/s10957-014-0572-0
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Elizabeth Karas & Elvio Pilotta & Ademir Ribeiro, 2009. "Numerical comparison of merit function with filter criterion in inexact restoration algorithms using hard-spheres problems," Computational Optimization and Applications, Springer, vol. 44(3), pages 427-441, December.
    4. C. Y. Kaya & J. M. Martínez, 2007. "Euler Discretization and Inexact Restoration for Optimal Control," Journal of Optimization Theory and Applications, Springer, vol. 134(2), pages 191-206, August.
    5. Juliano Francisco & J. Martínez & Leandro Martínez & Feodor Pisnitchenko, 2011. "Inexact restoration method for minimization problems arising in electronic structure calculations," Computational Optimization and Applications, Springer, vol. 50(3), pages 555-590, December.
    6. R. Andreani & S. Castro & J. Chela & A. Friedlander & S. Santos, 2009. "An inexact-restoration method for nonlinear bilevel programming problems," Computational Optimization and Applications, Springer, vol. 43(3), pages 307-328, July.
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    8. Regina Burachik & Alfredo Iusem & Jefferson Melo, 2010. "A primal dual modified subgradient algorithm with sharp Lagrangian," Journal of Global Optimization, Springer, vol. 46(3), pages 347-361, March.
    9. Regina Burachik & C. Kaya & Musa Mammadov, 2010. "An inexact modified subgradient algorithm for nonconvex optimization," Computational Optimization and Applications, Springer, vol. 45(1), pages 1-24, January.
    10. J.M. Martínez & B.F. Svaiter, 2003. "A Practical Optimality Condition Without Constraint Qualifications for Nonlinear Programming," Journal of Optimization Theory and Applications, Springer, vol. 118(1), pages 117-133, July.
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    Cited by:

    1. Juliano B. Francisco & Douglas S. Gonçalves & Fermín S. V. Bazán & Lila L. T. Paredes, 2020. "Non-monotone inexact restoration method for nonlinear programming," Computational Optimization and Applications, Springer, vol. 76(3), pages 867-888, July.
    2. E. G. Birgin & L. F. Bueno & J. M. Martínez, 2016. "Sequential equality-constrained optimization for nonlinear programming," Computational Optimization and Applications, Springer, vol. 65(3), pages 699-721, December.

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