Nonmonotone Spectral Projected Gradient Methods on Convex Sets

Nonmonotone projected gradient techniques are considered for the minimization of differentiable functions on closed convex sets. The classical projected gradient schemes are extended to include a nonmonotone steplength strategy that is based on the Grippo--Lampariello--Lucidi nonmonotone line search...

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Bibliographic Details
Published in:SIAM journal on optimization 2000, Vol.10 (4), p.1196-1211
Main Authors: Birgin, Ernesto G., Martínez, José Mario, Raydan, Marcos
Format: Article
Language:English
Subjects:
Algorithms
Methods
Simplex method
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Summary:Nonmonotone projected gradient techniques are considered for the minimization of differentiable functions on closed convex sets. The classical projected gradient schemes are extended to include a nonmonotone steplength strategy that is based on the Grippo--Lampariello--Lucidi nonmonotone line search. In particular, the nonmonotone strategy is combined with the spectral gradient choice of steplength to accelerate the convergence process. In addition to the classical projected gradient nonlinear path, the feasible spectral projected gradient is used as a search direction to avoid additional trial projections during the one-dimensional search process. Convergence properties and extensive numerical results are presented.
ISSN:1052-6234
1095-7189
DOI:10.1137/S1052623497330963