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

Year: 2025

Type: article

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.

Source: edoc Publication server (Humboldt University of Berlin)

DOI: 10.18452/35940

Authors: Baumgärtner, Lukas, Bethke, Franz, Shyshkanova, Ganna, Walther, Andrea

Language: English

Topic: Optimization and Variational Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7125413681

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