A convex penalty for switching control of partial differential equations
Abstract
A convex penalty for promoting switching controls for partial differential equations is introduced; such controls consist of an arbitrary number of components of which at most one should be simultaneously active. Using a Moreau–Yosida approximation, a family of approximating problems is obtained that is amenable to solution by a semismooth Newton method. In conclusion, the efficiency of this approach and the structure of the obtained controls are demonstrated by numerical examples.
- Authors:
-
- Univ. of Duisburg-Essen, Essen (Germany)
- Karl-Franzens-Univ. Graz, Graz (Austria)
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Publication Date:
- Research Org.:
- Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1266013
- Grant/Contract Number:
- AC05-00OR22725
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Systems & Control Letters
- Additional Journal Information:
- Journal Volume: 89; Journal ID: ISSN 0167-6911
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; optimal control; switching control; partial differential equations; nonsmooth optimization; convex analysis; semi-smooth Newton method
Citation Formats
Clason, Christian, Rund, Armin, Kunisch, Karl, and Barnard, Richard C. A convex penalty for switching control of partial differential equations. United States: N. p., 2016.
Web. doi:10.1016/j.sysconle.2015.12.013.
Clason, Christian, Rund, Armin, Kunisch, Karl, & Barnard, Richard C. A convex penalty for switching control of partial differential equations. United States. https://doi.org/10.1016/j.sysconle.2015.12.013
Clason, Christian, Rund, Armin, Kunisch, Karl, and Barnard, Richard C. Tue .
"A convex penalty for switching control of partial differential equations". United States. https://doi.org/10.1016/j.sysconle.2015.12.013. https://www.osti.gov/servlets/purl/1266013.
@article{osti_1266013,
title = {A convex penalty for switching control of partial differential equations},
author = {Clason, Christian and Rund, Armin and Kunisch, Karl and Barnard, Richard C.},
abstractNote = {A convex penalty for promoting switching controls for partial differential equations is introduced; such controls consist of an arbitrary number of components of which at most one should be simultaneously active. Using a Moreau–Yosida approximation, a family of approximating problems is obtained that is amenable to solution by a semismooth Newton method. In conclusion, the efficiency of this approach and the structure of the obtained controls are demonstrated by numerical examples.},
doi = {10.1016/j.sysconle.2015.12.013},
journal = {Systems & Control Letters},
number = ,
volume = 89,
place = {United States},
year = {Tue Jan 19 00:00:00 EST 2016},
month = {Tue Jan 19 00:00:00 EST 2016}
}
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Works referencing / citing this record:
Stationarity conditions and constraint qualifications for mathematical programs with switching constraints: With applications to either-or-constrained programming
journal, March 2019
- Mehlitz, Patrick
- Mathematical Programming, Vol. 181, Issue 1
Optimal control problems with control complementarity constraints: existence results, optimality conditions, and a penalty method
journal, May 2019
- Clason, Christian; Deng, Yu; Mehlitz, Patrick
- Optimization Methods and Software, Vol. 35, Issue 1
Hybrid Optimal Control Problems for a Class of Semilinear Parabolic Equations
preprint, January 2016
- Court, Sébastien; Kunisch, Karl; Pfeiffer, Laurent
- arXiv
A Hybrid Finite-Dimensional RHC for Stabilization of Time-Varying Parabolic Equations
preprint, January 2019
- Azmi, Behzad; Kunisch, Karl
- arXiv