## Casas, Eduardo

Compute Distance To:
 Author ID: casas.eduardo Published as: Casas, Eduardo; Casas, E.; Casa, Eduardo more...less External Links: ORCID · ResearchGate
 Documents Indexed: 158 Publications since 1982 4 Contributions as Editor Reviewing Activity: 27 Reviews Biographic References: 1 Publication Co-Authors: 35 Co-Authors with 132 Joint Publications 1,406 Co-Co-Authors
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### Co-Authors

 30 single-authored 33 Tröltzsch, Fredi 27 Mateos, Mariano 17 Kunisch, Karl 15 Fernández, Luis Alberto 11 Bonnans, Joseph Frédéric 7 Chrysafinos, Konstantinos 7 Raymond, Jean-Pierre 6 Rösch, Arnd 6 Wachsmuth, Gerd 4 Herzog, Roland 4 Pola, Cecilia 4 Unger, Andreas 3 Clason, Christian 3 Dhamo, Vili 3 Ryll, Christopher 3 Wachsmuth, Daniel 3 Yong, Jiongmin 2 Abergel, Frédéric 2 Leugering, Günter 2 Sokołowski, Jan 2 Vexler, Boris 2 Zidani, Housnaa 2 Zuazua, Enrique 1 Arada, Nadir 1 De los Reyes, Juan Carlos 1 de Teresa, Luz 1 Glowinski, Roland 1 Günther, Andreas 1 Kavian, Otared 1 Kogut, Peter I. 1 Kruse, Florian 1 Lobo, Miguel Sousa 1 Puel, Jean-Pierre 1 Trélat, Emmanuel 1 Zhou, Yong
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### Serials

 33 SIAM Journal on Control and Optimization 15 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 8 Applied Mathematics and Optimization 8 Control and Cybernetics 8 Computational Optimization and Applications 6 Numerische Mathematik 6 SIAM Journal on Optimization 6 Mathematical Control and Related Fields 3 Numerical Functional Analysis and Optimization 3 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 2 Journal of Mathematical Analysis and Applications 2 Journal of Differential Equations 2 Optimization 2 Vietnam Journal of Mathematics 1 Inverse Problems 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Analele Științifice ale Universității Al. I. Cuza din Iași. (Serie Nouă.) Secțiunea Ia. Matematică-Informatică 1 Manuscripta Mathematica 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 RAIRO. Recherche Opérationnelle 1 SIAM Journal on Numerical Analysis 1 Systems & Control Letters 1 Zeitschrift für Analysis und ihre Anwendungen 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Revista Matemática de la Universidad Complutense de Madrid 1 Differential and Integral Equations 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Computational and Applied Mathematics 1 Advances in Computational Mathematics 1 Computational Methods in Applied Mathematics 1 Lecture Notes in Pure and Applied Mathematics 1 Set-Valued and Variational Analysis 1 S$$\vec{\text{e}}$$MA Journal 1 Boletín de la Sociedad Española de Matemática Aplicada. S$$\vec{\text{e}}$$MA
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### Fields

 140 Calculus of variations and optimal control; optimization (49-XX) 106 Partial differential equations (35-XX) 33 Numerical analysis (65-XX) 23 Systems theory; control (93-XX) 13 Operations research, mathematical programming (90-XX) 8 Fluid mechanics (76-XX) 4 General and overarching topics; collections (00-XX) 3 Functional analysis (46-XX) 2 Algebraic geometry (14-XX) 2 Dynamical systems and ergodic theory (37-XX) 1 History and biography (01-XX) 1 Commutative algebra (13-XX) 1 Real functions (26-XX) 1 Mechanics of deformable solids (74-XX)

### Citations contained in zbMATH Open

125 Publications have been cited 2,328 times in 994 Documents Cited by Year
Error estimates for the numerical approximation of a semilinear elliptic control problem. Zbl 1033.65044
2002
Control of an elliptic problem with pointwise state constraints. Zbl 0606.49017
Casas, Eduardo
1986
Pontryagin’s principle for state-constrained boundary control problems of semilinear parabolic equations. Zbl 0893.49017
Casas, Eduardo
1997
Boundary control of semilinear elliptic equations with pointwise state constraints. Zbl 0798.49020
Casas, Eduardo
1993
Error estimates for the numerical approximation of Dirichlet boundary control for semilinear elliptic equations. Zbl 1123.65061
Casas, Eduardo; Raymond, Jean-Pierre
2006
Sufficient second-order optimality conditions for semilinear control problems with pointwise state constraints. Zbl 1161.49019
Casas, Eduardo; De Los Reyes, Juan Carlos; Tröltzsch, Fredi
2008
Error estimates for the numerical approximation of boundary semilinear elliptic control problems. Zbl 1081.49023
Casas, Eduardo; Mateos, Mariano; Tröltzsch, Fredi
2005
Approximation of elliptic control problems in measure spaces with sparse solutions. Zbl 1343.49048
Casas, Eduardo; Clason, Christian; Kunisch, Karl
2012
Parabolic control problems in measure spaces with sparse solutions. Zbl 1266.49037
Casas, Eduardo; Clason, Christian; Kunisch, Karl
2013
Optimality conditions and error analysis of semilinear elliptic control problems with $$L^1$$ cost functional. Zbl 1278.49026
Casas, Eduardo; Herzog, Roland; Wachsmuth, Gerd
2012
Second order optimality conditions for semilinear elliptic control problems with finitely many state constraints. Zbl 1037.49024
Casas, Eduardo; Mateos, Mariano
2002
Uniform convergence of the FEM applications to state constrained control problems. Zbl 1119.49309
Casas, Eduardo; Mateos, Mariano
2002
Second-order necessary and sufficient optimality conditions for optimization problems and applications to control theory. Zbl 1052.49022
Casas, Eduardo; Tröltzsch, Fredi
2002
Second order analysis for bang-bang control problems of PDEs. Zbl 1257.49021
Casas, Eduardo
2012
$$L^ 2$$ estimates for the finite element method for the Dirichlet problem with singular data. Zbl 0561.65071
Casas, Eduardo
1985
Error estimates for the numerical approximation of semilinear elliptic control problems with finitely many state constraints. Zbl 1066.49018
Casas, Eduardo
2002
Second order analysis for optimal control problems: improving results expected from abstract theory. Zbl 1259.90162
Casas, Eduardo; Tröltzsch, Fredi
2012
Second order optimality conditions and their role in PDE control. Zbl 1311.49002
Casas, Eduardo; Tröltzsch, Fredi
2015
Using piecewise linear functions in the numerical approximation of semilinear elliptic control problems. Zbl 1118.65069
Casas, Eduardo
2007
Error estimates for the numerical approximation of a distributed control problem for the steady-state Navier-Stokes equations. Zbl 1163.76028
Casas, Eduardo; Mateos, Mariano; Raymond, Jean-Pierre
2007
First- and second-order optimality conditions for a class of optimal control problems with quasilinear elliptic equations. Zbl 1194.49025
Casas, Eduardo; Tröltzsch, Fredi
2009
An extension of Pontryagin’s principle for state-constrained optimal control of semilinear elliptic equations and variational inequalities. Zbl 0821.49018
Bonnans, Frédéric; Casas, Eduardo
1995
Sparse optimal control of the Schlögl and Fitzhugh-Nagumo systems. Zbl 1393.49019
Casas, Eduardo; Ryll, Christopher; Tröltzsch, Fredi
2013
New regularity results and improved error estimates for optimal control problems with state constraints. Zbl 1293.49044
Casas, Eduardo; Mateos, Mariano; Vexler, Boris
2014
Error estimates for the numerical approximation of Neumann control problems. Zbl 1191.49030
Casas, Eduardo; Mateos, Mariano
2008
Pontryagin’s principle for local solutions of control problems with mixed control-state constraints. Zbl 0984.49011
Casas, E.; Raymond, J.-P.; Zidani, H.
2000
Error estimates for the finite-element approximation of a semilinear elliptic control problem. Zbl 1126.49315
Casas, Eduardo; Tröltzsch, Fredi
2002
Second order sufficient optimality conditions for some state-constrained control problems of semilinear elliptic equations. Zbl 0962.49016
Casas, Eduardo; Tröltzsch, Fredi; Unger, Andreas
2000
Second-order necessary optimality conditions for some state-constrained control problems of semilinear elliptic equations. Zbl 0921.49013
Casas, E.; Tröltzsch, F.
1999
Distributed control of systems governed by a general class of quasilinear elliptic equations. Zbl 0798.49021
Casa, Eduardo; Fernández, Luis Alberto
1993
A Green’s formula for quasilinear elliptic operators. Zbl 0704.35047
Casas, Eduardo; Fernández, Luis Alberto
1989
Regularization by functions of bounded variation and applications to image enhancement. Zbl 0942.49014
Casas, E.; Kunisch, K.; Pola, C.
1999
Optimal control in coefficients of elliptic equations with state constraints. Zbl 0769.49003
Casas, Eduardo
1992
Penalization of Dirichlet optimal control problems. Zbl 1175.49027
Casas, Eduardo; Mateos, Mariano; Raymond, Jean-Pierre
2009
Second order and stability analysis for optimal sparse control of the Fitzhugh-Nagumo equation. Zbl 1326.49032
Casas, Eduardo; Ryll, Christopher; Tröltzsch, Fredi
2015
Optimal control of semilinear elliptic equations in measure spaces. Zbl 1306.90172
Casas, Eduardo; Kunisch, Karl
2014
Spike controls for elliptic and parabolic PDEs. Zbl 1267.49005
Casas, E.; Zuazua, E.
2013
Optimal control of semilinear multistate systems with state constraints. Zbl 0667.49014
Bonnans, Joseph Frederic; Casas, Eduardo
1989
Some optimal control problems of multistate equations appearing in fluid mechanics. Zbl 0769.49002
Abergel, Frederic; Casas, Eduardo
1993
Sparse initial data identification for parabolic PDE and its finite element approximations. Zbl 1327.35131
Casas, Eduardo; Vexler, Boris; Zuazua, Enrique
2015
Error estimates for linear-quadratic elliptic control problems. Zbl 1027.65088
Casas, Eduardo; Tröltzsch, Fredi
2003
Parabolic control problems in space-time measure spaces. Zbl 1343.49036
Casas, Eduardo; Kunisch, Karl
2016
Analysis of spatio-temporally sparse optimal control problems of semilinear parabolic equations. Zbl 1479.49047
Casas, Eduardo; Herzog, Roland; Wachsmuth, Gerd
2017
Optimal control of semilinear elliptic equations with pointwise constraints on the gradient of the state. Zbl 0761.49010
Casas, Eduardo; Fernández, Luis Alberto
1993
Second order sufficient optimality conditions for a nonlinear elliptic boundary control problem. Zbl 0879.49020
Casas, E.; Tröltzsch, F.; Unger, A.
1996
Approximation of sparse controls in semilinear equations by piecewise linear functions. Zbl 1284.65074
Casas, Eduardo; Herzog, Roland; Wachsmuth, Gerd
2012
Approximation of optimal control problems in the coefficient for the $$p$$-Laplace equation. I: Convergence result. Zbl 1341.35075
Casas, Eduardo; Kogut, Peter I.; Leugering, Günter
2016
A discontinuous Galerkin time-stepping scheme for the velocity tracking problem. Zbl 1273.49035
Casas, Eduardo; Chrysafinos, Konstantinos
2012
Sufficient second-order conditions for bang-bang control problems. Zbl 1378.49019
Casas, Eduardo; Wachsmuth, Daniel; Wachsmuth, Gerd
2017
A general theorem on error estimates with application to a quasilinear elliptic optimal control problem. Zbl 1264.49030
Casas, Eduardo; Tröltzsch, Fredi
2012
Analysis of the velocity tracking control problem for the 3D evolutionary Navier-Stokes equations. Zbl 1408.49002
Casas, Eduardo; Chrysafinos, Konstantinos
2016
A review on sparse solutions in optimal control of partial differential equations. Zbl 1391.35124
Casas, Eduardo
2017
Recent advances in the analysis of pointwise state-constrained elliptic optimal control problems. Zbl 1201.49004
Casas, Eduardo; Tröltzsch, Fredi
2010
Optimal control of partial differential equations. Zbl 1391.49037
Casas, Eduardo; Mateos, Mariano
2017
Second-order and stability analysis for state-constrained elliptic optimal control problems with sparse controls. Zbl 1306.90173
Casas, Eduardo; Tröltzsch, Fredi
2014
Optimal control of quasilinear elliptic equations with non differentiable coefficients at the origin. Zbl 0749.49006
Casas, Eduardo; Fernández, Luis Alberto
1991
Optimality conditions for some control problems of turbulent flows. Zbl 0864.49018
Casas, Eduardo
1995
Pontryagin’s principle for the control of parabolic equations with gradient state constraints. Zbl 0998.49014
Casas, E.; Mateos, M.; Raymond, J.-P.
2001
Optimal control of an ill-posed elliptic semilinear equation with an exponential nonlinearity. Zbl 0911.49003
Casas, E.; Kavian, O.; Puel, J.-P.
1998
Optimal control of quasilinear parabolic equations. Zbl 0833.49002
Casas, Eduardo; Fernández, Luis A.; Yong, Jiongmin
1995
Error estimates for the numerical approximation of Neumann control problems governed by a class of quasilinear elliptic equations. Zbl 1260.49049
Casas, Eduardo; Dhamo, Vili
2012
Second-order optimality conditions for weak and strong local solutions of parabolic optimal control problems. Zbl 1337.49038
Casas, Eduardo; Tröltzsch, Fredi
2016
Second-order analysis and numerical approximation for bang-bang bilinear control problems. Zbl 1403.49017
Casas, Eduardo; Wachsmuth, Daniel; Wachsmuth, Gerd
2018
Maximum principle for state-constrained optimal control problems governed by quasilinear elliptic equations. Zbl 0817.49025
Casas, Eduardo; Yong, Jiongmin
1995
Un principe de Pontryagine pour le contrôle des systèmes semilinéaires elliptiques. (A Pontryagin principle for control of semilinear elliptic systems). Zbl 0742.93035
Bonnans, Joseph Frédéric; Casas, Eduardo
1991
Contrôle de systèmes elliptiques semilinéaires comportant des contraintes sur l’état. (Control of semilinear elliptic systems with state constraints). Zbl 0656.49011
Bonnans, J. F.; Casas, E.
1988
Optimal control of semilinear parabolic equations by BV-functions. Zbl 1365.35077
Casas, Eduardo; Kruse, Florian; Kunisch, Karl
2017
Numerical analysis of some optimal control problems governed by a class of quasilinear elliptic equations. Zbl 1228.49033
Casas, Eduardo; Tröltzsch, Fredi
2011
Approximation of boundary control problems on curved domains. Zbl 1203.49007
Casas, Eduardo; Sokolowski, Jan
2010
Error estimates for the numerical approximation of a quaslinear Neumann problem under minimal regularity of the data. Zbl 1209.65129
Casas, Eduardo; Dhamo, Vili
2011
Necessary and sufficient optimality conditions for elliptic control problems with finitely many pointwise state constraints. Zbl 1357.49089
Casas, Eduardo
2008
Optimality conditions for a class of optimal boundary control problems with quasilinear elliptic equations. Zbl 1318.49036
Casas, Eduardo; Dhamo, Vili
2011
Stabilization by sparse controls for a class of semilinear parabolic equations. Zbl 1372.35152
Casas, Eduardo; Kunisch, Karl
2017
Analysis and optimal control of some quasilinear parabolic equations. Zbl 1416.35145
Casas, Eduardo; Chrysafinos, Konstantinos
2018
On the singularities of polar curves. Zbl 0526.14015
Casas, Eduardo
1983
Finite element approximation of sparse parabolic control problems. Zbl 1369.49006
Casas, Eduardo; Mateos, Mariano; Rösch, Arnd
2017
Error estimates for semilinear parabolic control problems in the absence of Tikhonov term. Zbl 1420.35138
Casas, Eduardo; Mateos, Mariano; Rösch, Arnd
2019
Pontryagin’s principle for optimal control problems governed by semilinear elliptic equations. Zbl 0810.49025
Casas, Eduardo
1994
Dealing with integral state constraints in boundary control problems of quasilinear elliptic equations. Zbl 0858.49017
Casas, Eduardo; Fernández, Luis A.
1995
Critical cones for sufficient second order conditions in PDE constrained optimization. Zbl 1431.35077
Casas, Eduardo; Mateos, Mariano
2020
A paradox in the approximation of Dirichlet control problems in curved domains. Zbl 1234.49005
Casas, Eduardo; Günther, Andreas; Mateos, Mariano
2011
Optimal control of the two-dimensional stationary Navier-Stokes equations with measure valued controls. Zbl 1433.49037
Casas, Eduardo; Kunisch, Karl
2019
The stability in $$W^{s,p}(\Gamma)$$ spaces of $$L^2$$-projections on some convex sets. Zbl 1112.65064
Casas, Eduardo; Raymond, J.-P.
2006
Error estimates for the discretization of the velocity tracking problem. Zbl 1426.76232
Casas, Eduardo; Chrysafinos, Konstantinos
2015
Improved approximation rates for a parabolic control problem with an objective promoting directional sparsity. Zbl 1391.49038
Casas, Eduardo; Mateos, Mariano; Rösch, Arnd
2018
Error estimates for the approximation of the velocity tracking problem with bang-bang controls. Zbl 1388.49003
Casas, Eduardo; Chrysafinos, Konstantinos
2017
The relaxation theory applied to optimal control problems of semilinear elliptic equations. Zbl 0880.49032
Casas, Eduardo
1996
On the choice of the function spaces for some state-constrained control problems. Zbl 0589.49016
Bonnans, J. F.; Casas, E.
1985
Numerical approximation of elliptic control problems with finitely many pointwise constraints. Zbl 1244.49051
Casas, Eduardo; Mateos, Mariano
2012
Optimal control problem governed by semilinear elliptic equations with integral control constraints and pointwise state constraints. Zbl 0906.49010
Casas, E.; Raymond, J.-P.; Zidani, H.
1998
Necessary and sufficient optimality conditions for optimization problems in function spaces and applications to control theory. Zbl 1034.49020
Casas, E.; Mateos, Mariano; Tröltzsch, Fredi
2003
The Navier-Stokes equations coupled with the heat equation: Analysis and control. Zbl 0901.49003
Casas, Eduardo
1994
A boundary Pontryagin’s principle for the optimal control of state- constrained elliptic systems. Zbl 0769.49017
Bonnans, J. Frédéric; Casas, Eduardo
1992
Boundary control problems for quasi-linear elliptic equations: A Pontryagin’s principle. Zbl 0868.49017
Casas, E.
1996
Optimality conditions and numerical approximations for some optimal design problems. Zbl 0731.49010
Casas, Eduardo
1990
Numerical analysis of quasilinear parabolic equations under low regularity assumptions. Zbl 1427.65239
Casas, Eduardo; Chrysafinos, Konstantinos
2019
Analysis of optimal control problems of semilinear elliptic equations by BV-functions. Zbl 1421.35124
Casas, Eduardo; Kunisch, Karl
2019
Corrigendum: Optimal control of semilinear elliptic equations with pointwise constraints on the gradient of the state. Zbl 0781.49015
Casas, Eduardo; Fernández, Luis Alberto
1993
Moduli of algebroid plane curves. Zbl 0515.14019
Casas, E.
1982
Quelques problèmes de contrôle avec contraintes sur l’etat. Zbl 0522.49003
Casas, Eduardo
1983
Optimal control of semilinear parabolic equations with non-smooth pointwise-integral control constraints in time-space. Zbl 1485.35270
Casas, Eduardo; Kunisch, Karl
2022
Optimal control of the two-dimensional evolutionary Navier-Stokes equations with measure valued controls. Zbl 1477.35119
Casas, Eduardo; Kunisch, Karl
2021
Well-posedness of evolutionary Navier-Stokes equations with forces of low regularity on two-dimensional domains. Zbl 1475.35226
Casas, Eduardo; Kunisch, Karl
2021
State error estimates for the numerical approximation of sparse distributed control problems in the absence of Tikhonov regularization. Zbl 1473.35242
Casas, Eduardo; Mateos, Mariano
2021
Critical cones for sufficient second order conditions in PDE constrained optimization. Zbl 1431.35077
Casas, Eduardo; Mateos, Mariano
2020
First and second order conditions for optimal control problems with an $$L^0$$ term in the cost functional. Zbl 1454.35147
Casas, Eduardo; Wachsmuth, Daniel
2020
Sparse optimal control for the heat equation with mixed control-state constraints. Zbl 1455.49013
Casas, Eduardo; Tröltzsch, Fredi
2020
Analysis of control problems of nonmontone semilinear elliptic equations. Zbl 1460.35150
Casas, Eduardo; Mateos, Mariano; Rösch, Arnd
2020
Error estimates for semilinear parabolic control problems in the absence of Tikhonov term. Zbl 1420.35138
Casas, Eduardo; Mateos, Mariano; Rösch, Arnd
2019
Optimal control of the two-dimensional stationary Navier-Stokes equations with measure valued controls. Zbl 1433.49037
Casas, Eduardo; Kunisch, Karl
2019
Numerical analysis of quasilinear parabolic equations under low regularity assumptions. Zbl 1427.65239
Casas, Eduardo; Chrysafinos, Konstantinos
2019
Analysis of optimal control problems of semilinear elliptic equations by BV-functions. Zbl 1421.35124
Casas, Eduardo; Kunisch, Karl
2019
Using sparse control methods to identify sources in linear diffusion-convection equations. Zbl 1447.35376
Casas, Eduardo; Kunisch, Karl
2019
Optimal time delays in a class of reaction-diffusion equations. Zbl 1407.49025
Casas, E.; Mateos, M.; Tröltzsch, F.
2019
Optimal sparse boundary control for a semilinear parabolic equation with mixed control-state constraints. Zbl 1451.49024
Casas, Eduardo; Tröltzsch, Fredi
2019
Second-order analysis and numerical approximation for bang-bang bilinear control problems. Zbl 1403.49017
Casas, Eduardo; Wachsmuth, Daniel; Wachsmuth, Gerd
2018
Analysis and optimal control of some quasilinear parabolic equations. Zbl 1416.35145
Casas, Eduardo; Chrysafinos, Konstantinos
2018
Improved approximation rates for a parabolic control problem with an objective promoting directional sparsity. Zbl 1391.49038
Casas, Eduardo; Mateos, Mariano; Rösch, Arnd
2018
Optimal control of a class of reaction-diffusion systems. Zbl 1397.49031
Casas, Eduardo; Ryll, Christopher; Tröltzsch, Fredi
2018
The influence of the Tikhonov term in optimal control of partial differential equations. Zbl 1417.35212
Casas, Eduardo
2018
Analysis of spatio-temporally sparse optimal control problems of semilinear parabolic equations. Zbl 1479.49047
Casas, Eduardo; Herzog, Roland; Wachsmuth, Gerd
2017
Sufficient second-order conditions for bang-bang control problems. Zbl 1378.49019
Casas, Eduardo; Wachsmuth, Daniel; Wachsmuth, Gerd
2017
A review on sparse solutions in optimal control of partial differential equations. Zbl 1391.35124
Casas, Eduardo
2017
Optimal control of partial differential equations. Zbl 1391.49037
Casas, Eduardo; Mateos, Mariano
2017
Optimal control of semilinear parabolic equations by BV-functions. Zbl 1365.35077
Casas, Eduardo; Kruse, Florian; Kunisch, Karl
2017
Stabilization by sparse controls for a class of semilinear parabolic equations. Zbl 1372.35152
Casas, Eduardo; Kunisch, Karl
2017
Finite element approximation of sparse parabolic control problems. Zbl 1369.49006
Casas, Eduardo; Mateos, Mariano; Rösch, Arnd
2017
Error estimates for the approximation of the velocity tracking problem with bang-bang controls. Zbl 1388.49003
Casas, Eduardo; Chrysafinos, Konstantinos
2017
Parabolic control problems in space-time measure spaces. Zbl 1343.49036
Casas, Eduardo; Kunisch, Karl
2016
Approximation of optimal control problems in the coefficient for the $$p$$-Laplace equation. I: Convergence result. Zbl 1341.35075
Casas, Eduardo; Kogut, Peter I.; Leugering, Günter
2016
Analysis of the velocity tracking control problem for the 3D evolutionary Navier-Stokes equations. Zbl 1408.49002
Casas, Eduardo; Chrysafinos, Konstantinos
2016
Second-order optimality conditions for weak and strong local solutions of parabolic optimal control problems. Zbl 1337.49038
Casas, Eduardo; Tröltzsch, Fredi
2016
A review of numerical analysis for the discretization of the velocity tracking problem. Zbl 06981849
Casas, Eduardo; Chrysafinos, Konstantinos
2016
Second order optimality conditions and their role in PDE control. Zbl 1311.49002
Casas, Eduardo; Tröltzsch, Fredi
2015
Second order and stability analysis for optimal sparse control of the Fitzhugh-Nagumo equation. Zbl 1326.49032
Casas, Eduardo; Ryll, Christopher; Tröltzsch, Fredi
2015
Sparse initial data identification for parabolic PDE and its finite element approximations. Zbl 1327.35131
Casas, Eduardo; Vexler, Boris; Zuazua, Enrique
2015
Error estimates for the discretization of the velocity tracking problem. Zbl 1426.76232
Casas, Eduardo; Chrysafinos, Konstantinos
2015
New regularity results and improved error estimates for optimal control problems with state constraints. Zbl 1293.49044
Casas, Eduardo; Mateos, Mariano; Vexler, Boris
2014
Optimal control of semilinear elliptic equations in measure spaces. Zbl 1306.90172
Casas, Eduardo; Kunisch, Karl
2014
Second-order and stability analysis for state-constrained elliptic optimal control problems with sparse controls. Zbl 1306.90173
Casas, Eduardo; Tröltzsch, Fredi
2014
Editorial. Fractional systems and optimization. Zbl 1298.00198
2014
Parabolic control problems in measure spaces with sparse solutions. Zbl 1266.49037
Casas, Eduardo; Clason, Christian; Kunisch, Karl
2013
Sparse optimal control of the Schlögl and Fitzhugh-Nagumo systems. Zbl 1393.49019
Casas, Eduardo; Ryll, Christopher; Tröltzsch, Fredi
2013
Spike controls for elliptic and parabolic PDEs. Zbl 1267.49005
Casas, E.; Zuazua, E.
2013
Approximation of elliptic control problems in measure spaces with sparse solutions. Zbl 1343.49048
Casas, Eduardo; Clason, Christian; Kunisch, Karl
2012
Optimality conditions and error analysis of semilinear elliptic control problems with $$L^1$$ cost functional. Zbl 1278.49026
Casas, Eduardo; Herzog, Roland; Wachsmuth, Gerd
2012
Second order analysis for bang-bang control problems of PDEs. Zbl 1257.49021
Casas, Eduardo
2012
Second order analysis for optimal control problems: improving results expected from abstract theory. Zbl 1259.90162
Casas, Eduardo; Tröltzsch, Fredi
2012
Approximation of sparse controls in semilinear equations by piecewise linear functions. Zbl 1284.65074
Casas, Eduardo; Herzog, Roland; Wachsmuth, Gerd
2012
A discontinuous Galerkin time-stepping scheme for the velocity tracking problem. Zbl 1273.49035
Casas, Eduardo; Chrysafinos, Konstantinos
2012
A general theorem on error estimates with application to a quasilinear elliptic optimal control problem. Zbl 1264.49030
Casas, Eduardo; Tröltzsch, Fredi
2012
Error estimates for the numerical approximation of Neumann control problems governed by a class of quasilinear elliptic equations. Zbl 1260.49049
Casas, Eduardo; Dhamo, Vili
2012
Numerical approximation of elliptic control problems with finitely many pointwise constraints. Zbl 1244.49051
Casas, Eduardo; Mateos, Mariano
2012
Approximation of sparse controls in semilinear elliptic equations. Zbl 1310.49004
Casas, Eduardo; Herzog, Roland; Wachsmuth, Gerd
2012
Numerical analysis of some optimal control problems governed by a class of quasilinear elliptic equations. Zbl 1228.49033
Casas, Eduardo; Tröltzsch, Fredi
2011
Error estimates for the numerical approximation of a quaslinear Neumann problem under minimal regularity of the data. Zbl 1209.65129
Casas, Eduardo; Dhamo, Vili
2011
Optimality conditions for a class of optimal boundary control problems with quasilinear elliptic equations. Zbl 1318.49036
Casas, Eduardo; Dhamo, Vili
2011
A paradox in the approximation of Dirichlet control problems in curved domains. Zbl 1234.49005
Casas, Eduardo; Günther, Andreas; Mateos, Mariano
2011
Recent advances in the analysis of pointwise state-constrained elliptic optimal control problems. Zbl 1201.49004
Casas, Eduardo; Tröltzsch, Fredi
2010
Approximation of boundary control problems on curved domains. Zbl 1203.49007
Casas, Eduardo; Sokolowski, Jan
2010
First- and second-order optimality conditions for a class of optimal control problems with quasilinear elliptic equations. Zbl 1194.49025
Casas, Eduardo; Tröltzsch, Fredi
2009
Penalization of Dirichlet optimal control problems. Zbl 1175.49027
Casas, Eduardo; Mateos, Mariano; Raymond, Jean-Pierre
2009
Error estimates in the approximation of boundary control problems on curved domains. Zbl 1193.49019
Casas, Eduardo; Sokolowski, Jan
2009
Sufficient second-order optimality conditions for semilinear control problems with pointwise state constraints. Zbl 1161.49019
Casas, Eduardo; De Los Reyes, Juan Carlos; Tröltzsch, Fredi
2008
Error estimates for the numerical approximation of Neumann control problems. Zbl 1191.49030
Casas, Eduardo; Mateos, Mariano
2008
Necessary and sufficient optimality conditions for elliptic control problems with finitely many pointwise state constraints. Zbl 1357.49089
Casas, Eduardo
2008
Using piecewise linear functions in the numerical approximation of semilinear elliptic control problems. Zbl 1118.65069
Casas, Eduardo
2007
Error estimates for the numerical approximation of a distributed control problem for the steady-state Navier-Stokes equations. Zbl 1163.76028
Casas, Eduardo; Mateos, Mariano; Raymond, Jean-Pierre
2007
Error estimates for the numerical approximation of Dirichlet boundary control for semilinear elliptic equations. Zbl 1123.65061
Casas, Eduardo; Raymond, Jean-Pierre
2006
The stability in $$W^{s,p}(\Gamma)$$ spaces of $$L^2$$-projections on some convex sets. Zbl 1112.65064
Casas, Eduardo; Raymond, J.-P.
2006
Error estimates for the numerical approximation of boundary semilinear elliptic control problems. Continuous piecewise linear approximations. Zbl 1214.49019
Casas, E.; Mateos, M.
2006
Error estimates for the numerical approximation of boundary semilinear elliptic control problems. Zbl 1081.49023
Casas, Eduardo; Mateos, Mariano; Tröltzsch, Fredi
2005
Error estimates for linear-quadratic elliptic control problems. Zbl 1027.65088
Casas, Eduardo; Tröltzsch, Fredi
2003
Necessary and sufficient optimality conditions for optimization problems in function spaces and applications to control theory. Zbl 1034.49020
Casas, E.; Mateos, Mariano; Tröltzsch, Fredi
2003
Error estimates for the numerical approximation of a semilinear elliptic control problem. Zbl 1033.65044
2002
Second order optimality conditions for semilinear elliptic control problems with finitely many state constraints. Zbl 1037.49024
Casas, Eduardo; Mateos, Mariano
2002
Uniform convergence of the FEM applications to state constrained control problems. Zbl 1119.49309
Casas, Eduardo; Mateos, Mariano
2002
Second-order necessary and sufficient optimality conditions for optimization problems and applications to control theory. Zbl 1052.49022
Casas, Eduardo; Tröltzsch, Fredi
2002
Error estimates for the numerical approximation of semilinear elliptic control problems with finitely many state constraints. Zbl 1066.49018
Casas, Eduardo
2002
Error estimates for the finite-element approximation of a semilinear elliptic control problem. Zbl 1126.49315
Casas, Eduardo; Tröltzsch, Fredi
2002
Pontryagin’s principle for the control of parabolic equations with gradient state constraints. Zbl 0998.49014
Casas, E.; Mateos, M.; Raymond, J.-P.
2001
Pontryagin’s principle for local solutions of control problems with mixed control-state constraints. Zbl 0984.49011
Casas, E.; Raymond, J.-P.; Zidani, H.
2000
Second order sufficient optimality conditions for some state-constrained control problems of semilinear elliptic equations. Zbl 0962.49016
Casas, Eduardo; Tröltzsch, Fredi; Unger, Andreas
2000
Second-order necessary optimality conditions for some state-constrained control problems of semilinear elliptic equations. Zbl 0921.49013
Casas, E.; Tröltzsch, F.
1999
Regularization by functions of bounded variation and applications to image enhancement. Zbl 0942.49014
Casas, E.; Kunisch, K.; Pola, C.
1999
Second-order optimality conditions for semilinear elliptic control problems with constraints on the gradient of the state. Zbl 0947.49019
Casas, E.; Fernández, L. A.; Mateos, M.
1999
Optimal control of an ill-posed elliptic semilinear equation with an exponential nonlinearity. Zbl 0911.49003
Casas, E.; Kavian, O.; Puel, J.-P.
1998
Optimal control problem governed by semilinear elliptic equations with integral control constraints and pointwise state constraints. Zbl 0906.49010
Casas, E.; Raymond, J.-P.; Zidani, H.
1998
Some applications of BV functions in optimal control and calculus of variations. Zbl 0908.49006
Casas, E.; Kunisch, K.; Pola, C.
1998
Pontryagin’s principle for state-constrained boundary control problems of semilinear parabolic equations. Zbl 0893.49017
Casas, Eduardo
1997
Second order sufficient optimality conditions for a nonlinear elliptic boundary control problem. Zbl 0879.49020
Casas, E.; Tröltzsch, F.; Unger, A.
1996
The relaxation theory applied to optimal control problems of semilinear elliptic equations. Zbl 0880.49032
Casas, Eduardo
1996
Boundary control problems for quasi-linear elliptic equations: A Pontryagin’s principle. Zbl 0868.49017
Casas, E.
1996
An extension of Pontryagin’s principle for state-constrained optimal control of semilinear elliptic equations and variational inequalities. Zbl 0821.49018
Bonnans, Frédéric; Casas, Eduardo
1995
Optimality conditions for some control problems of turbulent flows. Zbl 0864.49018
Casas, Eduardo
1995
Optimal control of quasilinear parabolic equations. Zbl 0833.49002
Casas, Eduardo; Fernández, Luis A.; Yong, Jiongmin
1995
Maximum principle for state-constrained optimal control problems governed by quasilinear elliptic equations. Zbl 0817.49025
Casas, Eduardo; Yong, Jiongmin
1995
Dealing with integral state constraints in boundary control problems of quasilinear elliptic equations. Zbl 0858.49017
Casas, Eduardo; Fernández, Luis A.
1995
Pontryagin’s principle for optimal control problems governed by semilinear elliptic equations. Zbl 0810.49025
Casas, Eduardo
1994
The Navier-Stokes equations coupled with the heat equation: Analysis and control. Zbl 0901.49003
Casas, Eduardo
1994
...and 25 more Documents
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### Cited by 985 Authors

 66 Casas, Eduardo 45 Tröltzsch, Fredi 43 Kunisch, Karl 36 Rösch, Arnd 35 Chen, Yanping 27 Wachsmuth, Daniel 24 Mateos, Mariano 23 Vexler, Boris 21 Lu, Zuliang 18 Neitzel, Ira 16 Hinze, Michael 16 Meyer, Christian 16 Wachsmuth, Gerd 15 Alvarez-Vázquez, Lino Jose 15 Otárola, Enrique 14 Wollner, Winnifried 13 Clason, Christian 13 Gong, Wei 13 Martinez, Aurea 12 Bonnans, Joseph Frédéric 12 Brenner, Susanne Cecelia 12 De los Reyes, Juan Carlos 12 Raymond, Jean-Pierre 11 Hou, Tianliang 11 Yan, Ningning 10 Apel, Thomas 10 Huang, Yunqing 9 Borzì, Alfio 9 Kogut, Peter I. 9 Pfefferer, Johannes 9 Vázquez-Méndez, Miguel Ernesto 9 Yousept, Irwin 9 Zuazua, Enrique 8 Bergounioux, Maïtine 8 Guan, Hongbo 8 Herzog, Roland 8 Kupenko, Olha P. 8 Papageorgiou, Nikolaos S. 8 Sinha, Rajen Kumar 8 Tang, Yuelong 8 Volkwein, Stefan 8 Wang, Gengsheng 7 Allendes, Alejandro 7 Antil, Harbir 7 García-Chan, Néstor 7 Gudi, Thirupathi 7 Hintermüller, Michael 7 Huang, Fenglin 7 Kien, Bui Trong 7 Luan, Shu 7 Mallea-Zepeda, Exequiel 7 Nhu, Vu Huu 7 Pieper, Konstantin 7 Salgado, Abner J. 7 Schiela, Anton 7 Trélat, Emmanuel 7 Zhou, Jianwei 6 Aronna, María Soledad 6 Chen, Qihong 6 Chrysafinos, Konstantinos 6 Fernández, Francisco Javier 6 Günther, Andreas 6 Manzo, Rosanna 6 Merino, Pedro 6 Rehberg, Joachim 6 Serovaĭskiĭ, Simon Ya. 6 Shi, Dongyang 6 Sumin, Mikhail Iosifovich 6 Tanaka, Mieko 6 Trautmann, Philip 6 Zhou, Zhaojie 5 Bonifacius, Lucas 5 Christof, Constantin 5 Gao, Hang 5 Gugat, Martin 5 Kaltenbacher, Barbara 5 Kröner, Axel 5 Kumar, Sarvesh 5 Lin, Xiuxiu 5 Liu, Steve Wenbin 5 Maksimov, Vyacheslav Ivanovich 5 Mohan, Manil Thankamani 5 Nataraj, Neela 5 Sandilya, Ruchi 5 Shakya, Pratibha 5 Singler, John R. 5 Sprekels, Jürgen 5 Steinbach, Olaf 5 Villamizar-Roa, Elder Jesús 5 Walter, Daniel 5 Winkler, Max 5 Yang, Danping 5 Ye, Yuquan 5 Zhang, Yangwen 5 Zhang, Zhiyue 4 Arada, Nadir 4 Chang, Lili 4 Chowdhury, Sudipto Paul 4 Deckelnick, Klaus 4 Dhamo, Vili ...and 885 more Authors
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### Cited in 192 Serials

 66 Computational Optimization and Applications 60 SIAM Journal on Control and Optimization 52 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 34 Numerical Functional Analysis and Optimization 31 Journal of Mathematical Analysis and Applications 30 Numerische Mathematik 29 Journal of Optimization Theory and Applications 28 Applied Mathematics and Optimization 28 Mathematical Control and Related Fields 27 Computers & Mathematics with Applications 22 Journal of Computational and Applied Mathematics 21 Journal of Scientific Computing 18 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 16 SIAM Journal on Numerical Analysis 16 Applied Numerical Mathematics 15 Applied Mathematics and Computation 14 Applicable Analysis 13 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 12 Optimization 11 Journal of Differential Equations 11 Optimization Methods & Software 10 Inverse Problems 10 Zeitschrift für Analysis und ihre Anwendungen 9 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 8 Numerical Algorithms 8 SIAM Journal on Optimization 8 Journal of Inequalities and Applications 8 Advances in Applied Mathematics and Mechanics 8 Set-Valued and Variational Analysis 8 Evolution Equations and Control Theory 7 Systems & Control Letters 7 Computational Methods in Applied Mathematics 6 Mathematical Methods in the Applied Sciences 6 Automatica 6 Optimal Control Applications & Methods 6 Vietnam Journal of Mathematics 6 Boundary Value Problems 5 Mathematics of Computation 5 International Journal of Computer Mathematics 5 SIAM Journal on Scientific Computing 5 Optimization and Engineering 5 Lobachevskii Journal of Mathematics 5 Nonlinear Analysis. Real World Applications 5 Journal of Applied Mathematics and Computing 5 East Asian Journal on Applied Mathematics 4 Computer Methods in Applied Mechanics and Engineering 4 International Journal of Control 4 Journal of the Franklin Institute 4 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 4 Russian Mathematics 4 Calculus of Variations and Partial Differential Equations 4 Journal of Inverse and Ill-Posed Problems 4 Abstract and Applied Analysis 4 Positivity 4 Discrete and Continuous Dynamical Systems. Series B 4 Journal of Systems Science and Complexity 4 International Journal of Numerical Analysis and Modeling 4 GAMM-Mitteilungen 4 SIAM Journal on Imaging Sciences 4 Science China. Mathematics 3 Journal of Computational Physics 3 Calcolo 3 Numerical Methods for Partial Differential Equations 3 Journal of Global Optimization 3 Advances in Computational Mathematics 3 Mathematical Problems in Engineering 3 Journal of Mathematical Fluid Mechanics 3 Communications in Contemporary Mathematics 3 Frontiers of Mathematics in China 3 Optimization Letters 2 Mathematical Notes 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Compositio Mathematica 2 International Journal for Numerical Methods in Engineering 2 Journal of Functional Analysis 2 Kodai Mathematical Journal 2 Results in Mathematics 2 Ricerche di Matematica 2 Chinese Annals of Mathematics. Series B 2 Acta Applicandae Mathematicae 2 RAIRO. Modélisation Mathématique et Analyse Numérique 2 Acta Mathematicae Applicatae Sinica. English Series 2 Applied Mathematics Letters 2 Computational Mathematics and Modeling 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 Mathematical Programming. Series A. Series B 2 Journal of Convex Analysis 2 Opuscula Mathematica 2 European Journal of Control 2 Taiwanese Journal of Mathematics 2 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 2 Communications in Nonlinear Science and Numerical Simulation 2 International Journal of Applied Mathematics and Computer Science 2 The ANZIAM Journal 2 Differential Equations 2 Journal of Numerical Mathematics 2 Communications on Pure and Applied Analysis 2 Multiscale Modeling & Simulation 2 Advances in Difference Equations ...and 92 more Serials
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### Cited in 42 Fields

 781 Calculus of variations and optimal control; optimization (49-XX) 478 Partial differential equations (35-XX) 419 Numerical analysis (65-XX) 115 Operations research, mathematical programming (90-XX) 115 Systems theory; control (93-XX) 78 Fluid mechanics (76-XX) 31 Biology and other natural sciences (92-XX) 29 Mechanics of deformable solids (74-XX) 28 Operator theory (47-XX) 14 Classical thermodynamics, heat transfer (80-XX) 13 Global analysis, analysis on manifolds (58-XX) 11 Functional analysis (46-XX) 10 Probability theory and stochastic processes (60-XX) 10 Information and communication theory, circuits (94-XX) 9 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 8 Ordinary differential equations (34-XX) 7 Algebraic geometry (14-XX) 7 Dynamical systems and ergodic theory (37-XX) 7 Computer science (68-XX) 6 Optics, electromagnetic theory (78-XX) 5 Several complex variables and analytic spaces (32-XX) 5 Integral equations (45-XX) 4 Real functions (26-XX) 4 Approximations and expansions (41-XX) 3 Quantum theory (81-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 General and overarching topics; collections (00-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Convex and discrete geometry (52-XX) 2 Differential geometry (53-XX) 2 Mechanics of particles and systems (70-XX) 2 Geophysics (86-XX) 1 History and biography (01-XX) 1 Mathematical logic and foundations (03-XX) 1 Combinatorics (05-XX) 1 Category theory; homological algebra (18-XX) 1 Measure and integration (28-XX) 1 Potential theory (31-XX) 1 Integral transforms, operational calculus (44-XX) 1 General topology (54-XX) 1 Statistics (62-XX)