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Inexact-Restoration Algorithm for Constrained Optimization1

Author

Listed:
  • J. M. Martínez

    (University of Campinas)

  • E. A. Pilotta

    (University of Campinas)

Abstract

We introduce a new model algorithm for solving nonlinear programming problems. No slack variables are introduced for dealing with inequality constraints. Each iteration of the method proceeds in two phases. In the first phase, feasibility of the current iterate is improved; in second phase, the objective function value is reduced in an approximate feasible set. The point that results from the second phase is compared with the current point using a nonsmooth merit function that combines feasibility and optimality. This merit function includes a penalty parameter that changes between consecutive iterations. A suitable updating procedure for this penalty parameter is included by means of which it can be increased or decreased along consecutive iterations. The conditions for feasibility improvement at the first phase and for optimality improvement at the second phase are mild, and large-scale implementation of the resulting method is possible. We prove that, under suitable conditions, which do not include regularity or existence of second derivatives, all the limit points of an infinite sequence generated by the algorithm are feasible, and that a suitable optimality measure can be made as small as desired. The algorithm is implemented and tested against the LANCELOT algorithm using a set of hard-spheres problems.

Suggested Citation

  • J. M. Martínez & E. A. Pilotta, 2000. "Inexact-Restoration Algorithm for Constrained Optimization1," Journal of Optimization Theory and Applications, Springer, vol. 104(1), pages 135-163, January.
    • Handle: RePEc:spr:joptap:v:104:y:2000:i:1:d:10.1023_a:1004632923654
    DOI: 10.1023/A:1004632923654
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    Citations

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    Cited by:

    1. Wolfgang Schadner, 2021. "Feasible Implied Correlation Matrices from Factor Structures," Papers 2107.00427, arXiv.org.
    2. J. M. Martínez, 2001. "Inexact-Restoration Method with Lagrangian Tangent Decrease and New Merit Function for Nonlinear Programming," Journal of Optimization Theory and Applications, Springer, vol. 111(1), pages 39-58, October.
    3. R. Andreani & E. H. Fukuda & G. Haeser & D. O. Santos & L. D. Secchin, 2021. "On the use of Jordan Algebras for improving global convergence of an Augmented Lagrangian method in nonlinear semidefinite programming," Computational Optimization and Applications, Springer, vol. 79(3), pages 633-648, July.
    4. 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.
    5. Cândida Silva & M. Monteiro, 2008. "A filter inexact-restoration method for nonlinear programming," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(1), pages 126-146, July.
    6. Wolfgang Schadner & Joshua Traut, 2022. "Estimating Forward-Looking Stock Correlations from Risk Factors," Mathematics, MDPI, vol. 10(10), pages 1-19, May.

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