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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.19437 |
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Table of Contents:
- We consider constraints on the measure of the support for integrable functions on arbitrary measure spaces. It is shown that this non-convex and discontinuous constraint can be equivalently reformulated by the difference of two convex and continuous functions, namely the $L^1$-norm and the so-called largest-$K$-norm. The largest-$K$-norm is studied and its convex subdifferential is derived. A corresponding penalty method is proposed, and its numerical solution by a DC method is investigated. Numerical experiments for two example problems, including a sparse optimal control problem, are presented.