On the worst-case complexity of nonlinear stepsize control algorithms for convex unconstrained optimization

Abstract

A Nonlinear Stepsize Control (NSC) framework has been proposed by Toint [Nonlinear stepsize control, trust regions and regularizations for unconstrained optimization, Optim.Methods Softw. 28 (2013), pp. 82–95] for unconstrained optimization, generalizing many trust-region and regularization algorithms. More recently, worst-case complexity bounds for the generic NSC framework were proved by Grapiglia et al. [On the convergence and worst-case complexity of trust-region and regularization methods for unconstrained optimization, Math. Program. 152 (2015), pp. 491–520] in the context of non-convex problems. In this paper, improved complexity bounds are obtained for convex and strongly convex objectives.