Nonlinear Stepsize Control Algorithms: Complexity Bounds for First- and Second-Order Optimality
Volume: 171 • Number: 3 • Pages: 980-997
A nonlinear stepsize control (NSC) framework has been proposed by Toint (Optim Methods Softw 28:82–95, 2013) for unconstrained optimization, generalizing several trust-region and regularization algorithms. More recently, worst-case complexity bounds to achieve approximate first-order optimality were proved by Grapiglia, Yuan and Yuan (Math Program 152:491–520, 2015) for the generic NSC framework. In this paper, improved complexity bounds for first-order optimality are obtained. Furthermore, complexity bounds for second-order optimality are also provided.