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Augmented Lagrangian Algorithms Based on the Spectral Projected Gradient Method for Solving Nonlinear Programming Problems

Author

Listed:
  • M. A. Diniz-Ehrhardt

    (IMECC-UNICAMP)

  • M. A. Gomes-Ruggiero

    (IMECC-UNICAMP)

  • J. M. Martínez

    (IMECC-UNICAMP)

  • S. A. Santos

    (IMECC-UNICAMP)

Abstract

The spectral projected gradient method SPG is an algorithm for large-scale bound-constrained optimization introduced recently by Birgin, Martínez, and Raydan. It is based on the Raydan unconstrained generalization of the Barzilai-Borwein method for quadratics. The SPG algorithm turned out to be surprisingly effective for solving many large-scale minimization problems with box constraints. Therefore, it is natural to test its perfomance for solving the sub-problems that appear in nonlinear programming methods based on augmented Lagrangians. In this work, augmented Lagrangian methods which use SPG as the underlying convex-constraint solver are introduced (ALSPG) and the methods are tested in two sets of problems. First, a meaningful subset of large-scale nonlinearly constrained problems of the CUTE collection is solved and compared with the perfomance of LANCELOT. Second, a family of location problems in the minimax formulation is solved against the package FFSQP.

Suggested Citation

  • M. A. Diniz-Ehrhardt & M. A. Gomes-Ruggiero & J. M. Martínez & S. A. Santos, 2004. "Augmented Lagrangian Algorithms Based on the Spectral Projected Gradient Method for Solving Nonlinear Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 123(3), pages 497-517, December.
    • Handle: RePEc:spr:joptap:v:123:y:2004:i:3:d:10.1007_s10957-004-5720-5
    DOI: 10.1007/s10957-004-5720-5
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    Citations

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    Cited by:

    1. Birgin, Ernesto G. & Martínez, Jose Mario & Raydan, Marcos, 2014. "Spectral Projected Gradient Methods: Review and Perspectives," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 60(i03).
    2. H. Z. Luo & X. L. Sun & Y. F. Xu, 2010. "Convergence Properties of Modified and Partially-Augmented Lagrangian Methods for Mathematical Programs with Complementarity Constraints," Journal of Optimization Theory and Applications, Springer, vol. 145(3), pages 489-506, June.
    3. Torrealba, E.M.R. & Silva, J.G. & Matioli, L.C. & Kolossoski, O. & Santos, P.S.M., 2022. "Augmented Lagrangian algorithms for solving the continuous nonlinear resource allocation problem," European Journal of Operational Research, Elsevier, vol. 299(1), pages 46-59.
    4. Huixian Wu & Hezhi Luo & Xiaodong Ding & Guanting Chen, 2013. "Global convergence of modified augmented Lagrangian methods for nonlinear semidefinite programming," Computational Optimization and Applications, Springer, vol. 56(3), pages 531-558, December.

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