Semidiscrete Ritz-Galerkin approximation of nonlinear parabolic boundary control problems -- strong convergence of optimal controls
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Publication:1322719
DOI10.1007/BF01189480zbMath0802.49017OpenAlexW144579591MaRDI QIDQ1322719
Publication date: 5 May 1994
Published in: Applied Mathematics and Optimization (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf01189480
Optimality conditions for problems involving partial differential equations (49K20) Numerical optimization and variational techniques (65K10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)
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Cites Work
- Unnamed Item
- Unnamed Item
- On the approximation of infinite optimization problems with an application to optimal control problems
- Parabolic evolution equations and nonlinear boundary conditions
- Boundary control of parabolic systems: Finite-element approximation
- Unified theory for abstract parabolic boundary problems - a semigroup approach
- Convergence of approximations vs. regularity of solutions for convex, control-constrained optimal-control problems
- A unified theory of necessary conditions for nonlinear nonconvex control systems
- Second-Order Sufficient Optimality Conditions for a Class of Nonlinear Parabolic Boundary Control Problems
- Necessary and Sufficient Conditions for a Local Minimum. 3: Second Order Conditions and Augmented Duality
- Approximation of non-linear parabolic boundary control problems by the Fourier method - convergence of optimal control
- Galerkin Approximations of Abstract Parabolic Boundary Value Problems With Rough Boundary Data-L p Theory
- First and second order sufficient optimality conditions in mathematical programming and optimal control
- Finite Element Approximation of Parabolic Time Optimal Control Problems
- Some Convergence Estimates for Semidiscrete Galerkin Type Approximations for Parabolic Equations
- Convergence of Finite Element Approximations to State Constrained Convex Parabolic Boundary Control Problems
- On Convergence of Semidiscrete Ritz‐Galerkin Schemes Applied to the Boundary Control of Parabolic Equations with Non‐Linear Boundary Condition
- Second order optimality conditions for a class of control problems governed by non-linear integral equations with application to parabolic boundary control
- Dirichlet Boundary Control Problem for Parabolic Equations with Quadratic Cost: Analyticity and Riccati’s Feedback Synthesis
