Convergence of Linesearch and Trust-Region Methods Using the Kurdyka-Łojasiewicz Inequality

Abstract

We discuss backtracking linesearch and trust-region descent algorithms for unconstrained optimization and prove convergence to a critical point if the objective is of class C1 and satisfies the Kurdyka-Łojasiewicz condition. For linesearch we investigate in which way an intelligent management memorizing the stepsize should be organized. For trust-regions we present a new curvature-based acceptance test which ensures convergence under rather weak assumptions. © Springer Science+Business Media New York 2013.