tangential stationarity – Optimization Online

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

Published: 2017/12/22

Nonsmooth Optimization abs-normal form, active set and signature, karush kuhn tucker (kkt), linear independence kink qualification (likq), normal growth, quadratic regularization, successive piecewise linear optimization (splop), tangential stationarity

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

Published: 2015/11/06, Updated: 2016/03/11

Andreas Griewank

Andrea Walther

Nonsmooth Optimization, Unconstrained Optimization abs-normal form, karush-kuhn-tucker, normal growth, piecewise linearization, projected hessian, second-order optimality, tangential stationarity, u-v shape

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