Nonmonotone Spectral Projected Gradient Methods on Convex Sets

Abstract Nonmonotone projected gradient techniques are considered for the minimizationof differentiable functions on closed convex sets. The classical projected gradient schemes are extended to include a nonmonotone steplength strategy that is based onthe Grippo-Lampariello-Lucidi nonmonotone line search. In particular, the nonmonotone strategy is combined with the spectral gradient choice of steplength to acceleratethe convergence process. In addition to the classical projected gradient nonlinear path, the feasible spectral projected gradient is used as a search direction to avoid additionaltrial projections during the one-dimensional search process. Convergence properties and extensive numerical results are presented. Key words: Projected gradients, nonmonotone line search, large scale problems,bound constrained problems, spectral gradient method.