Convergence analysis of smoothing methods for optimal control of stationary variational inequalities with control constraints
ESAIM: M2AN, 47 3 (2013) 771-787
Published online: 2013-03-04
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
Boundary optimal control problems for parabolic variational inequalities of bilateral obstacle type
Zijia Peng, Sheng Huang and Zhenhai LiuJournal of Mathematical Analysis and Applications 542 (1) 128764 (2025)
https://doi.org/10.1016/j.jmaa.2024.128764
Optimal control of elliptic obstacle problems with mixed boundary conditions
Zijia Peng, Sheng Huang and Dailing ChaiOptimization 73 (5) 1397 (2024)
https://doi.org/10.1080/02331934.2022.2157679
Optimal control of an elastic–rigid obstacle problem
Qinghua Ran and Jie ZhangCommunications in Nonlinear Science and Numerical Simulation 132 107935 (2024)
https://doi.org/10.1016/j.cnsns.2024.107935
A Descent Algorithm for the Optimal Control of ReLU Neural Network Informed PDEs Based on Approximate Directional Derivatives
Guozhi Dong, Michael Hintermüller and Kostas PapafitsorosSIAM Journal on Optimization 34 (3) 2314 (2024)
https://doi.org/10.1137/22M1534420
Bilevel Optimization of the Kantorovich Problem and Its Quadratic Regularization
Sebastian Hillbrecht, Paul Manns and Christian MeyerApplied Mathematics & Optimization 90 (1) (2024)
https://doi.org/10.1007/s00245-024-10162-1
On solving elliptic obstacle problems by constant abs-linearization
Olga Weiß and Monika WeymuthResults in Control and Optimization 13 100309 (2023)
https://doi.org/10.1016/j.rico.2023.100309
A dynamical method for optimal control of the obstacle problem
Qinghua Ran, Xiaoliang Cheng, Rongfang Gong and Ye ZhangJournal of Inverse and Ill-posed Problems (2023)
https://doi.org/10.1515/jiip-2020-0135
First Order Limiting Optimality Conditions in the Coefficient Control of an Obstacle Problem
Nicolai Simon and Winnifried WollnerPAMM 22 (1) (2023)
https://doi.org/10.1002/pamm.202200184
Non-Smooth and Complementarity-Based Distributed Parameter Systems
Volker H. Schulz and Kathrin WelkerInternational Series of Numerical Mathematics, Non-Smooth and Complementarity-Based Distributed Parameter Systems 172 397 (2022)
https://doi.org/10.1007/978-3-030-79393-7_16
Strong stationarity for a highly nonsmooth optimization problem with control constraints
Livia BetzMathematical Control and Related Fields (2022)
https://doi.org/10.3934/mcrf.2022047
An Approximating Approach to an Optimal Control Problem for an Elliptic Variational Inequality on a Mixed Boundary⋆
Yarui Duan, Pengcheng Wu and Yuying ZhouNumerical Functional Analysis and Optimization 43 (9) 1095 (2022)
https://doi.org/10.1080/01630563.2022.2086570
The Boussinesq System with Nonsmooth Boundary Conditions: Existence, Relaxation, and Topology Optimization
Alexandre Vieira and Pierre-Henri CocquetSIAM Journal on Control and Optimization 60 (6) 3457 (2022)
https://doi.org/10.1137/21M1465159
Optimal Control and Directional Differentiability for Elliptic Quasi-Variational Inequalities
Amal Alphonse, Michael Hintermüller and Carlos N. RautenbergSet-Valued and Variational Analysis 30 (3) 873 (2022)
https://doi.org/10.1007/s11228-021-00624-x
Optimal control of friction coefficient in Signorini contact problems
El‐Hassan Essoufi and Abderrahim ZafrarOptimal Control Applications and Methods 42 (6) 1794 (2021)
https://doi.org/10.1002/oca.2765
On the Characterization of Generalized Derivatives for the Solution Operator of the Bilateral Obstacle Problem
Anne-Therese Rauls and Stefan UlbrichSIAM Journal on Control and Optimization 59 (5) 3683 (2021)
https://doi.org/10.1137/20M135916X
Geometric Partial Differential Equations - Part II
Michael Hintermüller and Tobias KeilHandbook of Numerical Analysis, Geometric Partial Differential Equations - Part II 22 213 (2021)
https://doi.org/10.1016/bs.hna.2020.10.003
On second-order optimality conditions for optimal control problems governed by the obstacle problem
Constantin Christof and Gerd WachsmuthOptimization 70 (10) 2247 (2021)
https://doi.org/10.1080/02331934.2020.1778686
Coupled versus decoupled penalization of control complementarity constraints
Yu Deng, Patrick Mehlitz and Uwe PrüfertESAIM: Control, Optimisation and Calculus of Variations 27 45 (2021)
https://doi.org/10.1051/cocv/2021022
Generalized Derivatives for the Solution Operator of the Obstacle Problem
Anne-Therese Rauls and Gerd WachsmuthSet-Valued and Variational Analysis 28 (2) 259 (2020)
https://doi.org/10.1007/s11228-019-0506-y
Efficient Techniques for Shape Optimization with Variational Inequalities Using Adjoints
Daniel Luft, Volker H. Schulz and Kathrin WelkerSIAM Journal on Optimization 30 (3) 1922 (2020)
https://doi.org/10.1137/19M1257226
Global minima for optimal control of the obstacle problem
Ahmad Ahmad Ali, Klaus Deckelnick and Michael HinzeESAIM: Control, Optimisation and Calculus of Variations 26 64 (2020)
https://doi.org/10.1051/cocv/2019039
Bilevel Optimization
Patrick Mehlitz and Gerd WachsmuthSpringer Optimization and Its Applications, Bilevel Optimization 161 451 (2020)
https://doi.org/10.1007/978-3-030-52119-6_16
Computation of a Bouligand Generalized Derivative for the Solution Operator of the Obstacle Problem
Anne-Therese Rauls and Stefan UlbrichSIAM Journal on Control and Optimization 57 (5) 3223 (2019)
https://doi.org/10.1137/18M1187283
An Optimal Control Problem Governed by a Regularized Phase-Field Fracture Propagation Model. Part II: The Regularization Limit
Ira Neitzel, Thomas Wick and Winnifried WollnerSIAM Journal on Control and Optimization 57 (3) 1672 (2019)
https://doi.org/10.1137/18M122385X
The limiting normal cone of a complementarity set in Sobolev spaces
Felix Harder and Gerd WachsmuthOptimization 67 (10) 1579 (2018)
https://doi.org/10.1080/02331934.2018.1484467
Comparison of optimality systems for the optimal control of the obstacle problem
Felix Harder and Gerd WachsmuthGAMM-Mitteilungen 40 (4) 312 (2018)
https://doi.org/10.1002/gamm.201740004
Adaptive optimal control of Signorini’s problem
Andreas Rademacher and Korinna RosinComputational Optimization and Applications 70 (2) 531 (2018)
https://doi.org/10.1007/s10589-018-9982-5
A bundle-free implicit programming approach for a class of elliptic MPECs in function space
M. Hintermüller and T. SurowiecMathematical Programming 160 (1-2) 271 (2016)
https://doi.org/10.1007/s10107-016-0983-9
Strong Stationarity Conditions for a Class of Optimization Problems Governed by Variational Inequalities of the Second Kind
J. C. De los Reyes and C. MeyerJournal of Optimization Theory and Applications 168 (2) 375 (2016)
https://doi.org/10.1007/s10957-015-0748-2
Towards M-stationarity for Optimal Control of the Obstacle Problem with Control Constraints
Gerd WachsmuthSIAM Journal on Control and Optimization 54 (2) 964 (2016)
https://doi.org/10.1137/140980582
Numerical Analysis and Optimization
M. Hintermüller, C. Löbhard and M. H. TberSpringer Proceedings in Mathematics & Statistics, Numerical Analysis and Optimization 134 151 (2015)
https://doi.org/10.1007/978-3-319-17689-5_7
Adaptive Optimal Control of the Obstacle Problem
Ch. Meyer, A. Rademacher and W. WollnerSIAM Journal on Scientific Computing 37 (2) A918 (2015)
https://doi.org/10.1137/140975863
Trends in PDE Constrained Optimization
Michael Hintermüller, Antoine Laurain, Caroline Löbhard, Carlos N. Rautenberg and Thomas M. SurowiecInternational Series of Numerical Mathematics, Trends in PDE Constrained Optimization 165 133 (2014)
https://doi.org/10.1007/978-3-319-05083-6_9
Strong Stationarity for Optimal Control of the Obstacle Problem with Control Constraints
Gerd WachsmuthSIAM Journal on Optimization 24 (4) 1914 (2014)
https://doi.org/10.1137/130925827
Trends in PDE Constrained Optimization
Roland Herzog, Christian Meyer and Gerd WachsmuthInternational Series of Numerical Mathematics, Trends in PDE Constrained Optimization 165 27 (2014)
https://doi.org/10.1007/978-3-319-05083-6_4