A priori error estimates for state-constrained semilinear parabolic optimal control problems
DOI10.1007/s10957-018-1311-8zbMath1398.49021OpenAlexW2809030115WikidataQ129578322 ScholiaQ129578322MaRDI QIDQ1670092
Francesco Ludovici, Winnifried Wollner, Ira Neitzel
Publication date: 4 September 2018
Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10957-018-1311-8
optimal controlstate constraintssemilinear parabolic PDEpointwise in time constraintsspace-time a priori error estimates
Optimality conditions for problems involving partial differential equations (49K20) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) A priori estimates in context of PDEs (35B45) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Discrete approximations in optimal control (49M25) Semilinear parabolic equations (35K58)
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Cites Work
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- Error estimates for parabolic optimal control problems with control and state constraints
- Symmetric error estimates for discontinuous Galerkin approximations for an optimal control problem associated to semilinear parabolic PDE's
- Discrete maximal parabolic regularity for Galerkin finite element methods
- A priori error estimates for space-time finite element discretization of semilinear parabolic optimal control problems
- A priori \(L^2\)-discretization error estimates for the state in elliptic optimization problems with pointwise inequality state constraints
- Stability of semilinear elliptic optimal control problems with pointwise state constraints
- Approximation of a class of optimal control problems with order of convergence estimates
- Sharp \(L^{\infty}\)-error estimates for semilinear elliptic problems with free boundaries
- Second order sufficient optimality conditions for nonlinear parabolic control problems with state constraints
- A variational discretization concept in control constrained optimization: The linear-quadratic case
- Second order optimality conditions and their role in PDE control
- Uniform convergence of the FEM applications to state constrained control problems
- Optimal error estimates for finite element discretization of elliptic optimal control problems with finitely many pointwise state constraints
- On the \(H^1\)-stability of the \(L_2\)-projection onto finite element spaces
- Pontryagin's Principle For Local Solutions of Control Problems with Mixed Control-State Constraints
- Pointwise Best Approximation Results for Galerkin Finite Element Solutions of Parabolic Problems
- Variational Discretization of Parabolic Control Problems in the Presence of Pointwise State Constraints
- Optimal Control of a Parabolic Equation with Time-Dependent State Constraints
- A Priori Error Estimates for Finite Element Discretizations of Parabolic Optimization Problems with Pointwise State Constraints in Time
- Second-Order Sufficient Optimality Conditions for a Class of Nonlinear Parabolic Boundary Control Problems
- Optimization with PDE Constraints
- Convergence of discontinuous Galerkin approximations of an optimal control problem associated to semilinear parabolic PDE's
- A Priori Error Estimates for Space-Time Finite Element Discretization of Parabolic Optimal Control Problems Part I: Problems Without Control Constraints
- A Priori Error Estimates for Space-Time Finite Element Discretization of Parabolic Optimal Control Problems Part II: Problems with Control Constraints
- Sufficient Second-Order Optimality Conditions for Semilinear Control Problems with Pointwise State Constraints
- Pontryagin's Principle for State-Constrained Boundary Control Problems of Semilinear Parabolic Equations
- Second Order Optimality Conditions for Semilinear Elliptic Control Problems with Finitely Many State Constraints
- Second Order Sufficient Optimality Conditions for Parabolic Optimal Control Problems with Pointwise State Constraints
- Finite Element Discretization of State-Constrained Elliptic Optimal Control Problems with Semilinear State Equation
- A Priori Error Estimates for a Finite Element Discretization of Parabolic Optimization Problems with Pointwise Constraints in Time on Mean Values of the Gradient of the State
- The Mathematical Theory of Finite Element Methods
- Galerkin Finite Element Methods for Parabolic Problems