A generalized worst-case complexity analysis for non-monotone line searches (Q2028039)

In this paper , the authors consider the worst-case complexity of a generalized version of the non-monotone line search framework proposed in [\textit{E. W. Sachs} and \textit{S. M. Sachs}, Control Cybern. 40, No. 4, 1059--1075 (2011; Zbl 1318.49059)] for smooth unconstrained optimization problems. This framework is built upon a generalized Armijo rule in which the level of non-monotonicity is controlled by a sequence of non-negative real parameters. The authors obtain complexity bounds to achieve approximate first-order optimality even when this sequence is not summable.