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

M. A. Diniz-Ehrhardt, M. A. Gomes-Ruggiero, J. M. Martínez and S. A. Santos
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M. A. Diniz-Ehrhardt: IMECC-UNICAMP
M. A. Gomes-Ruggiero: IMECC-UNICAMP
J. M. Martínez: IMECC-UNICAMP
S. A. Santos: IMECC-UNICAMP

Journal of Optimization Theory and Applications, 2004, vol. 123, issue 3, No 3, 497-517

Abstract: 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.

Keywords: Augmented Lagrangian methods; projected gradient methods; nonmonotone line search; large-scale problems; bound-constrained problems; Barzilai-Borwein method (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10957-004-5720-5

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