piecewise smoothness – Optimization Online

An Algorithm for Nonsmooth Optimization by Successive Piecewise Linearization

Published: 2016/12/08

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

Combinatorial Structures in Nonlinear Programming

Published: 2002/05/10, Updated: 2002/05/18

Stefan Scholtes

Constrained Nonlinear Optimization, Nonsmooth Optimization, Robust Optimization combinatorial structures, nonlinear programming, piecewise smoothness, robust stochastic programming

Non-smoothness and non-convexity in optimization problems often arise because a combinatorial structure is imposed on smooth or convex data. The combinatorial aspect can be explicit, e.g. through the use of ”max”, ”min”, or ”if” statements in a model, or implicit as in the case of bilevel optimization where the combinatorial structure arises from the possible … Read more