On the worst-case evaluation complexity of non-monotone line search algorithms

A general class of non-monotone line search algorithms has been proposed by Sachs and Sachs (Control Cybern 40:1059-1075, 2011) for smooth unconstrained optimization, generalizing various non-monotone step size rules such as the modified Armijo rule of Zhang and Hager (SIAM J Optim 14:1043-1056, 2004). In this paper, the worst-case complexity of this class of non-monotone algorithms is studied. The analysis is carried out in the context of non-convex, convex and strongly convex objectives with Lipschitz continuous gradients. Despite de nonmonotonicity in the decrease of function values, the complexity bounds obtained agree in order with the bounds already established for monotone algorithms.