Nonmonotone spectral projected gradient methods on convex sets

Nonmonotone projected gradient techniques are considered for the minimizati on of differentiable functions on closed convex sets. The classical project ed gradient schemes are extended to include a nonmonotone steplength strate gy that is based on the Grippo-Lampariello-Lucidi nonmonotone line search. In particular, the nonmonotone strategy is combined with the spectral gradi ent 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 properti es and extensive numerical results are presented.