Staircase Compatibility and its Applications in Scheduling and Piecewise Linearization

We consider the clique problem with multiple-choice constraints (CPMC) and characterize a case where it is possible to give an efficient description of the convex hull of its feasible solutions. This new special case, which we call staircase compatibility, generalizes common properties in several applications and allows for a linear description of the integer feasible … Read more

Algorithmic Differentiation for Piecewise Smooth Functions: A Case Study for 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

First and second order optimality conditions for piecewise smooth objective functions

Any piecewise smooth function that is specified by an evaluation procedures involving smooth elemental functions and piecewise linear functions like min and max can be represented in the so-called abs-normal form. By an extension of algorithmic, or automatic differentiation, one can then compute certain first and second order derivative vectors and matrices that represent a … Read more