linear-independence-kink-qualification

On First and Second Order Optimality Conditions for Abs-Normal NLP

Published: 2019/03/06

Structured nonsmoothness is widely present in practical optimization. A particularly attractive class of nonsmooth problems, both from a theoretical and from an algorithmic perspective, are optimization problems in so-called abs-normal form as developed by Griewank and Walther. Here we generalize their theory for the unconstrained case to nonsmooth NLPs with equality and inequality constraints in … Read more

Characterizing and testing subdifferential regularity for piecewise smooth objective functions

Published: 2017/11/05

Andreas Griewank

Andrea Walther

Nonsmooth Optimization abs-normal form, clarke gradient, first-order-convexity, linear-independence-kink-qualification, mangasarin-fromovitz-kink-qualification, mordukhovich gradient, subdifferential regularity

Functions defined by evaluation programs involving smooth elementals and absolute values as well as the max- and min-operator are piecewise smooth. Using piecewise linearization we derived in [7] for this class of nonsmooth functions first and second order conditions for local optimality (MIN). They are necessary and sufficient, eespectively. These generalizations of the classical KKT … Read more