Monotone and nonmonotone trust-region-based algorithms for large scale unconstrained optimization problems
Two trust regions algorithms for unconstrained nonlinear optimization problems are presented: a monotone and a nonmonotone one. Both of them solve the trust region subproblem by the spectral projected gradient (SPG) method proposed by Birgin, Martínez and Raydan (in SIAM J. Optim. 10(4):1196–1211, <CitationRef CitationID="CR3">2000</CitationRef>). SPG is a nonmonotone projected gradient algorithm for solving large-scale convex-constrained optimization problems. It combines the classical projected gradient method with the spectral gradient choice of steplength and a nonmonotone line search strategy. The simplicity (only requires matrix-vector products, and one projection per iteration) and rapid convergence of this scheme fits nicely with globalization techniques based on the trust region philosophy, for large-scale problems. In the nonmonotone algorithm the trial step is evaluated by acceptance via a rule which can be considered a generalization of the well known fraction of Cauchy decrease condition and a generalization of the nonmonotone line search proposed by Grippo, Lampariello and Lucidi (in SIAM J. Numer. Anal. 23:707–716, <CitationRef CitationID="CR13">1986</CitationRef>). Convergence properties and extensive numerical results are presented. Our results establish the robustness and efficiency of the new algorithms. Copyright Springer Science+Business Media, LLC 2013
Year of publication: |
2013
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Authors: | Maciel, María ; Mendonça, María ; Verdiell, Adriana |
Published in: |
Computational Optimization and Applications. - Springer. - Vol. 54.2013, 1, p. 27-43
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Publisher: |
Springer |
Subject: | Trust-region subproblems | Spectral projected gradient method | Nonmonotone line search | Large scale problems |
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