How Stringent is the Linear Independence Kink Qualification in Abs-Smooth Optimization?
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917867063083008 |
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| author | Baumgärtner, Lukas Bethke, Franz Shyshkanova, Ganna Walther, Andrea |
| author_facet | Baumgärtner, Lukas Bethke, Franz Shyshkanova, Ganna Walther, Andrea |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_09175 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | How Stringent is the Linear Independence Kink Qualification in Abs-Smooth Optimization? Baumgärtner, Lukas Bethke, Franz Shyshkanova, Ganna Walther, Andrea Optimization and Control 49J52, 57N75 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. |
| title | How Stringent is the Linear Independence Kink Qualification in Abs-Smooth Optimization? |
| topic | Optimization and Control 49J52, 57N75 |
| url | https://arxiv.org/abs/2412.09175 |