An Algorithm for Piecewise Linear Optimization of Objective Functions in Abs-normal Form

In the paper [11] we derived first order (KKT) and second order (SSC) optimality conditions for functions defined by evaluation programs involving smooth elementals and absolute values. For this class of problems we showed in [12] that the natural algorithm of successive piecewise linear optimization with a proximal term (SPLOP) achieves a linear or even … 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