Andreas Griewank; Lipschitzian Piecewise Smooth Optimization

April 14, 2015, 4:00pm
GUG 220
Andreas Griewank, Institut für Mathematik, Humboldt University of Berlin.
Lipschitzian Piecewise Smooth Optimization

Abstract: We address the problem of minimizing objectives from the class of piecewise differentiable functions whose nonsmoothness can be encapsulated in the absolute value function. They possess local piecewise linear approximations with a discrepancy that can be bounded by a quadratic proximal term. This overestimating local model is continuous but generally nonconvex. It can be generated in its {\em abs-normal-form} by a minor extension of standard algorithmic differentiation tools. Here we demonstrate how the local model can be minimized by a bundle type method, which benefits from the availability of additional {\em gray-box-information} via the abs-normal form. In the convex case our algorithms realizes the consistent steepest descent trajectory for which finite convergence was established by Hirriart Urruty and Claude Lemarechal, specifically covering counter examples where steepest descent with exact line-search famously fails.