Hybrid nonmonotone spectral gradient method for the unconstrained minimization problem

Abstract

Nonmonotone spectral gradient (NSG) techniques are considered for unconstrained optimization of differentiable functions. They combine a nonmonotone step length strategy, that is based on the Grippo–Lampariello–Lucidi nonmonotone line search, with the spectral gradient choice of steplength. In this paper, we present a hybrid nonmonotone spectral gradient method. In each iteration after finding an acceptable point by NSG method, we employ an extrapolation step to find a even better point by using particle swarm optimization. Through specific assumptions, we prove the global convergence of our proposed algorithm