Year: 2025
Type: preprint
Abstract: Cardinality constraints in optimization are commonly of $L^0$-type, and they lead to sparsely supported optimizers. An efficient way of dealing with these constraints algorithmically, when the objective functional is convex, is reformulating the constraint using the difference of suitable $L^1$- and largest-$K$-norms and subsequently solving a sequence of penalized subproblems in the difference-of-convex (DC) class. We extend this DC-reformulation approach to problems with $L^0$-type cardinality constraints on the support of the gradients, \ie, problems where sparsity of the gradient and thus piecewise constant solutions are the target. We apply the resulting algorithm to a classical energy minimization problem, an optimal control problem, and an image reconstruction problem.
Source: arXiv (Cornell University)
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
Award: G8189396523
OpenAlex ID: W4415069701
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