Nonmonotone spectral projected gradient methods on convex sets. (English) Zbl 1047.90077

Birgin, Ernesto G.; Martínez, José Mario; Raydan, Marcos

SIAM J. Optim. 10, No. 4, 1196-1211 (2000).

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.

MSC:

90C52	Methods of reduced gradient type
65K05	Numerical mathematical programming methods
90C06	Large-scale problems in mathematical programming
90C20	Quadratic programming

Keywords:

projected gradients; nonmonotone line search; large-scale problems; bound constrained problems; spectral gradient method

Software:

LANCELOT