Sabrina Fiege – Optimization Online

Algorithmic Differentiation for Piecewise Smooth Functions: A Case Study for Robust Optimization

Published: 2017/02/28, Updated: 2017/03/07

Nonsmooth Optimization algorithmic differentiation, nonsmooth optimization, piecewise linearization, robust optimization

This paper presents a minimization method for Lipschitz continuous, piecewise smooth objective functions based on algorithmic differentiation (AD). We assume that all nondifferentiabilities are caused by abs(), min(), and max(). The optimization method generates successively piecewise linearizations in abs-normal form and solves these local subproblems by exploiting the resulting kink structure. Both, the generation of … Read more

An Algorithm for Nonsmooth Optimization by Successive Piecewise Linearization

Published: 2016/12/08

Sabrina Fiege

Andreas Griewank

Andrea Walther

Nonsmooth Optimization abs-normal form, algorithmic differentiation, clarke stationary, nonsmooth optimization, piecewise smoothness

We present an optimization method for Lipschitz continuous, piecewise smooth (PS) objective functions based on successive piecewise linearization. Since, in many realistic cases, nondifferentiabilities are caused by the occurrence of abs(), max(), and min(), we concentrate on these nonsmooth elemental functions. The method’s idea is to locate an optimum of a PS objective function by … Read more

On Lipschitz optimization based on gray-box piecewise linearization

Published: 2014/06/25, Updated: 2015/02/10

Nonsmooth Optimization abs-normal form, algorithmic differentiation, bundle method, piecewise linearity

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 … Read more