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Sparse optimal control of a quasilinear elliptic PDE in measure spaces

Hoppe, Fabian (2022) Sparse optimal control of a quasilinear elliptic PDE in measure spaces. 15th Viennese Conference on Optimal Control and Dynamic Games 2022, 2022-07-12 - 2022-07-15, Wien, Österreich.

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Abstract

We considern a sparse optimal control problem governed by a quasilinear elliptic PDE in measure spaces. Under rather general assumptions we prove existence of optimal controls and derive first-order necessary optimality conditions. Under additional assumptions also second-order necessary and sufficient optimality conditions are obtained. The key technique of our analysis is the application of the so-called Kirchhoff transform, i.e. a nonlinear superposition operator that allows to transform the quasilinear state equation into a linear one.

Item URL in elib:https://elib.dlr.de/192007/
Document Type:Conference or Workshop Item (Speech)
Additional Information:This research has been conducted while the auther was affiliated with University of Bonn, Institute for Numerical Simulation, and partially supported by DFG SFB 1060.
Title:Sparse optimal control of a quasilinear elliptic PDE in measure spaces
Authors:
AuthorsInstitution or Email of AuthorsAuthor's ORCID iDORCID Put Code
Hoppe, FabianUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Date:July 2022
Refereed publication:Yes
Open Access:Yes
Gold Open Access:No
In SCOPUS:No
In ISI Web of Science:No
Status:Published
Keywords:optimal control, sparse, quasilinear, optimality conditions
Event Title:15th Viennese Conference on Optimal Control and Dynamic Games 2022
Event Location:Wien, Österreich
Event Type:international Conference
Event Start Date:12 July 2022
Event End Date:15 July 2022
Organizer:Technische Universität Wien
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Space Transportation
DLR - Research area:Raumfahrt
DLR - Program:R RP - Space Transportation
DLR - Research theme (Project):R - Project Amadeus, R - Tasks SISTEC
Location: Köln-Porz
Institutes and Institutions:Institut of Simulation and Software Technology > High Performance Computing
Institute for Software Technology
Deposited By: Hoppe, Fabian
Deposited On:21 Dec 2022 09:36
Last Modified:24 Apr 2024 20:53

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