How Stringent is the Linear Independence Kink Qualification in Abs-Smooth Optimization?
Optimization and Control
2024-12-13 v1
Abstract
Abs-smooth functions are given by compositions of smooth functions and the evaluation of the absolute value. The linear independence kink qualification (LIKQ) is a fundamental assumption in optimization problems governed by these abs-smooth functions, generalizing the well-known LICQ from smooth optimization. In particular, provided that LIKQ holds it is possible to derive optimality conditions for abs-smooth optimization problems that can be checked in polynomial time. Utilizing tools from differential topology, namely a version of the jet-transversality theorem, it is shown that assuming LIKQ for all feasible points of an abs-smooth optimization problem is a generic assumption.
Cite
@article{arxiv.2412.09175,
title = {How Stringent is the Linear Independence Kink Qualification in Abs-Smooth Optimization?},
author = {Lukas Baumgärtner and Franz Bethke and Ganna Shyshkanova and Andrea Walther},
journal= {arXiv preprint arXiv:2412.09175},
year = {2024}
}