Convergence of approximations vs. regularity of solutions for convex, control-constrained optimal-control problems

From MaRDI portal

Publication:1161989

Jump to:navigation, search

DOI10.1007/BF01447752zbMath0479.49017OpenAlexW1996778903MaRDI QIDQ1161989

Kazimierz Malanowski

Publication date: 1982

Published in: Applied Mathematics and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01447752

zbMATH Keywords

boundary control finite elements parabolic systems distributed control regularity results convex, control-constrained optimal control problems Galerkin-type approximations Neumann-type boundary conditions projections on the set of admissible controls

Mathematics Subject Classification ID

Newton-type methods (49M15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items

Superconvergence Properties for Optimal Control Problems Discretized by Piecewise Linear and Discontinuous Functions, \textit{A priori} error analysis for optimal distributed control problem governed by the first order linear hyperbolic equation: \textit{hp}-streamline diffusion discontinuous Galerkin method, Finite-difference discretizations of quadratic control problems governed by ordinary elliptic differential equations, Semidiscrete approximations of optimal Robin boundary control problems constrained by semilinear parabolic PDE, Analysis and finite element approximations for distributed optimal control problems for implicit parabolic equations, A priori error estimates for elliptic optimal control problems with a bilinear state equation, High-order discretization and multigrid solution of elliptic nonlinear constrained optimal control problems, Abstract estimates of the rate of convergence for optimal control problems, A priori error estimates for the finite element discretization of optimal distributed control problems governed by the biharmonic operator, Adaptive finite element method for optimal control problem governed by linear quasiparabolic integrodifferential equations, A posteriori error estimates for a semidiscrete parabolic integrodifferential control on multimeshes, A multiscale finite element method for optimal control problems governed by the elliptic homogenization equations, Unnamed Item, Unnamed Item, A posteriori error estimates for optimal distributed control governed by the evolution equations, Error analysis for finite element approximation of parabolic Neumann boundary control problems, A Priori Mesh Grading for Distributed Optimal Control Problems, Discretization of Optimal Control Problems, A Priori Error Estimates for Space-Time Finite Element Discretization of Parabolic Optimal Control Problems, Multigrid methods for parabolic distributed optimal control problems, Reliable Error Estimates for Optimal Control of Linear Elliptic PDEs with Random Inputs, Multigrid second-order accurate solution of parabolic control-constrained problems, Mixed finite element method for a second order Dirichlet boundary control problem, A posteriori error estimates for control problems governed by nonlinear elliptic equations, Third order convergent time discretization for parabolic optimal control problems with control constraints, Error estimates for the discretization of state constrained convex control problems, Error estimates of fully discrete mixed finite element methods for semilinear quadratic parabolic optimal control problem, LP modelling for the time optimal control problem of the heat equation, Optimal control problem governed by a linear hyperbolic integro-differential equation and its finite element analysis, A priori error estimates for space-time finite element discretization of semilinear parabolic optimal control problems, A superconvergent scheme for a locking‐free FEM in a Timoshenko optimal control problem, Variational multiscale method for the optimal control problems of convection--diffusion--reaction equations, Convergence of discontinuous Galerkin approximations of an optimal control problem associated to semilinear parabolic PDE's, Optimal control in non-convex domains: a priori discretization error estimates, A posteriori error estimates of recovery type for distributed convex optimal control problems, A posteriori error estimates for parabolic optimal control problems with controls acting on lower dimensional manifolds, A \(C^0\) interior penalty method for the Dirichlet control problem governed by biharmonic operator, A two-grid discretization scheme for optimal control problems of elliptic equations, Recovery type superconvergence and a posteriori error estimates for control problems governed by Stokes equations, Error estimates of triangular mixed finite element methods for quasilinear optimal control problems, Finite element error estimates for Neumann boundary control problems on graded meshes, On saturation effects in the Neumann boundary control of elliptic optimal control problems, \(L^2\)-error estimates for Dirichlet and Neumann problems on anisotropic finite element meshes, Optimal control of the Stokes equations: conforming and non-conforming finite element methods under reduced regularity, Sufficient second-order optimality conditions for convex control constraints, ERROR ESTIMATES IN THE APPROXIMATION OF OPTIMIZATION PROBLEMS GOVERNED BY NONLINEAR OPERATORS, Mesh-independence and preconditioning for solving parabolic control problems with mixed control-state constraints, Approximation of non-linear parabolic boundary control problems by the Fourier method - convergence of optimal control, Temporally semidiscrete approximation of a Dirichlet boundary control for a fractional/normal evolution equation with a final observation, Regularity of solutions for an optimal control problem with mixed control-state constraints, Convergence rates for direct transcription of optimal control problems using collocation at Radau points, Finite Element Approximations of Parabolic Optimal Control Problems with Controls Acting on a Lower Dimensional Manifold, Full-discrete adaptive FEM for quasi-parabolic integro-differential PDE-constrained optimal control problem, Quasi-best approximation in optimization with PDE constraints, Discretization of elliptic control problems with time dependent parameters, Error estimates for linear-quadratic control problems with control constraints, Linear and Discontinuous Approximations for Optimal Control Problems, Parabolic optimal control problems with a quintic B-spline dynamic model, A finite element method for elliptic optimal control problem on a non-convex polygon with corner singularities, Optimal control under reduced regularity, A priori error estimates for a linearized fracture control problem, Numerical methods for nonlinear inverse problems, A posteriori error estimates for some model boundary control problems, Strong rates of convergence for a space-time discretization of the backward stochastic heat equation, and of a linear-quadratic control problem for the stochastic heat equation, Some remarks on the numerical solution of bang-bang type optimal control problems, On finite element approximation of variational inequalities arising from elliptic control problems, Error estimates for spectral approximation of flow optimal control problem with \(L^2 \)-norm control constraint, Superconvergence for Neumann boundary control problems governed by semilinear elliptic equations, Error estimates for the numerical approximation of boundary semilinear elliptic control prob\-lems, A multigrid scheme for elliptic constrained optimal control problems, Semidiscrete Ritz-Galerkin approximation of nonlinear parabolic boundary control problems -- strong convergence of optimal controls

Cites Work

Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Publication:1161989&oldid=13229844"