How Stringent is the Linear Independence Kink Qualification in Abs-Smooth Optimization?

Lukas Baumgärtner; Franz Bethke; Ganna Shyshkanova; Andrea Walther

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arXiv · 2412.09175

How Stringent is the Linear Independence Kink Qualification in Abs-Smooth Optimization?

Lukas Baumgärtner·Franz Bethke·Ganna Shyshkanova·Andrea Walther

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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.

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Lukas Baumgärtner, Franz Bethke, Ganna Shyshkanova, Andrea Walther. 2024-12-12. How Stringent is the Linear Independence Kink Qualification in Abs-Smooth Optimization?. https://arxiv.org/abs/2412.09175

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