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 abs-normal form, obtaining similar necessary and sufficient conditions of first and second order that are directly based on classical Karush-Kuhn-Tucker (KKT) theory for smooth NLPs. Several small examples illustrate the theoretical results. We also give some brief remarks on the intimate relationship of abs-normal NLPs with MPECs.
Insitute of Applied Mathematics Leibniz University Hannover Welfengarten 1 30167 Hannover March 2019