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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.<\/jats:p>","DOI":"10.1007\/s10957-025-02874-3","type":"journal-article","created":{"date-parts":[[2025,12,29]],"date-time":"2025-12-29T10:45:32Z","timestamp":1767005132000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["How Stringent is the Linear Independence Kink Qualification in Abs-Smooth Optimization?"],"prefix":"10.1007","volume":"208","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1007-4815","authenticated-orcid":false,"given":"Lukas","family":"Baumg\u00e4rtner","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0553-4242","authenticated-orcid":false,"given":"Franz","family":"Bethke","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0336-2803","authenticated-orcid":false,"given":"Ganna","family":"Shyshkanova","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3516-4641","authenticated-orcid":false,"given":"Andrea","family":"Walther","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,12,29]]},"reference":[{"key":"2874_CR1","doi-asserted-by":"publisher","first-page":"606","DOI":"10.1007\/s10957-012-0210-7","volume":"159","author":"D Dorsch","year":"2013","unstructured":"Dorsch, D., Jongen, H.T., Shikhman, V.: On intrinsic complexity of Nash equilibrium problems and bilevel optimization. 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