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Optimal Control of Bilateral Obstacle Problems

Authors:

Maïtine Bergounioux,

Suzanne LenhartAuthors Info & Claims

SIAM Journal on Control and Optimization, Volume 43, Issue 1

Pages 240 - 255

https://doi.org/10.1137/S0363012902416912

Published: 22 November 2019 Publication History

Abstract

We consider an optimal control problem where the state satisfies a bilateral elliptic variational inequality and the control functions are the upper and lower obstacles. We seek a state that is close to a desired profile and the H² norms of the obstacles are not too large. Existence results are given and an optimality system is derived. A particular case is studied that needs no compactness assumption, via a monotonicity method.

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Zheng XGao Q(2019)Optimal Control of Obstacle ProblemProceedings of the 2019 4th International Conference on Mathematics and Artificial Intelligence10.1145/3325730.3325761(189-194)Online publication date: 12-Apr-2019
https://dl.acm.org/doi/10.1145/3325730.3325761
Ghanem RNouri I(2017)Optimal Control of High-Order Elliptic Obstacle ProblemApplied Mathematics and Optimization10.1007/s00245-016-9358-076:3(465-500)Online publication date: 1-Dec-2017
https://dl.acm.org/doi/10.1007/s00245-016-9358-0
Farshbaf-Shaker M(2015)A Relaxation Approach to Vector-Valued Allen---Cahn MPEC ProblemsApplied Mathematics and Optimization10.1007/s00245-014-9282-072:2(325-351)Online publication date: 1-Oct-2015
https://dl.acm.org/doi/10.1007/s00245-014-9282-0
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Optimal Control of Bilateral Obstacle Problems

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cover image SIAM Journal on Control and Optimization

SIAM Journal on Control and Optimization Volume 43, Issue 1

2004

205 pages

ISSN:0363-0129

Issue’s Table of Contents

Publisher

Society for Industrial and Applied Mathematics

United States

Publication History

Published: 22 November 2019

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Zheng XGao Q(2019)Optimal Control of Obstacle ProblemProceedings of the 2019 4th International Conference on Mathematics and Artificial Intelligence10.1145/3325730.3325761(189-194)Online publication date: 12-Apr-2019
https://dl.acm.org/doi/10.1145/3325730.3325761
Ghanem RNouri I(2017)Optimal Control of High-Order Elliptic Obstacle ProblemApplied Mathematics and Optimization10.1007/s00245-016-9358-076:3(465-500)Online publication date: 1-Dec-2017
https://dl.acm.org/doi/10.1007/s00245-016-9358-0
Farshbaf-Shaker M(2015)A Relaxation Approach to Vector-Valued Allen---Cahn MPEC ProblemsApplied Mathematics and Optimization10.1007/s00245-014-9282-072:2(325-351)Online publication date: 1-Oct-2015
https://dl.acm.org/doi/10.1007/s00245-014-9282-0
Di Donato DMugnai D(2015)On a Highly Nonlinear Self-Obstacle Optimal Control ProblemApplied Mathematics and Optimization10.1007/s00245-014-9279-872:2(261-290)Online publication date: 1-Oct-2015
https://dl.acm.org/doi/10.1007/s00245-014-9279-8
Adly SBergounioux MAit Mansour M(2010)Optimal control of a quasi-variational obstacle problemJournal of Global Optimization10.1007/s10898-008-9366-y47:3(421-435)Online publication date: 1-Jul-2010
https://dl.acm.org/doi/10.1007/s10898-008-9366-y
Ye YChan CLee H(2009)The existence results for obstacle optimal control problemsApplied Mathematics and Computation10.1016/j.amc.2009.04.006214:2(451-456)Online publication date: 1-Aug-2009
https://dl.acm.org/doi/10.1016/j.amc.2009.04.006

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