An Exploratory Line Search for Piecewise Differentiable Objective Functions based on Algorithmic Differentiation

Abstract

Nonsmoothness is a typical characteristic of numerous objective functions in optimisation that arises from applications. The standard approach in algorithmic differentiation (AD) is to consider only differentiable functions that are defined by an evaluation program. We extend this functionality by allowing also the functions abs(), min() and max() during the function evaluation yielding piecewise differential nonlinear functions. We will define an evaluation procedure for these functions and employ ADOL‐C in an adapted gradient based optimisation method that was adjusted to the special properties of the objective functions considered here. First numerical results will be presented. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

On Lipschitz optimization based on gray-box piecewise linearization

“…More details on the realization of this algorithm can be found in [7]. This provides the line search in Algorithm 4.…”