A topological derivative-based algorithm to solve optimal control problems with \(L^0(\Omega)\) control cost
type: Item
instance of: scholarly article
title: A topological derivative-based algorithm to solve optimal control problems with \(L^0(\Omega)\) control cost
zbMATH Open document ID: 1546.49054
author: Daniel Wachsmuth
published in: Journal of Nonsmooth Analysis and Optimization
publication date: 2024-07-04T00:00:00Z
review text: The paper derives a novel descent method for PDE-constrained optimal control problems that involve the \(L^0\)-cost of the control, i.e., the measure of the support of the control. A fundamental tool is the topological derivative of the value function with respect to variations of the support. For instance, it is shown that the pointwise a.e. non-negativity of this topological derivative is a necessary optimality condition, and the construction of the descent direction is based on this derivative. As main result it is proved that the algorithm generates a minimizing sequence for the value function. Interesting numerical examples like a binary control problem are also included.
reviewed by: Florian Mannel
Mathematics Subject Classification ID: 49M05
Mathematics Subject Classification ID: 49K40
Mathematics Subject Classification ID: 65K10
zbMATH DE Number: 7876116
zbMATH Keywords: topological derivative
zbMATH Keywords: control support optimization
zbMATH Keywords: sparse optimal control
zbMATH Keywords: \(L^0\) optimization
MaRDI profile type: Publication
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DOI: 10.46298/JNSAO-2024-12366
description: scientific article; zbMATH DE number 7876116