arXiv subjects

Bastian Dittrich

Publications and source records attributed to Bastian Dittrich.

2 recordsLinked to original sources

arXiv2026

A DC-Reformulation for Gradient-$L^0$-Constrained Problems

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, i.e., problems where sparsity of the gradient and thus piecewise constant solutions are the target.

math.OC↗

arXiv2024

The Largest-$K$-Norm for General Measure Spaces and a DC Reformulation for $L^0$-Constrained Problems in Function Spaces

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.

math.OC↗