Displaying similar documents to “POD a-posteriori error based inexact SQP method for bilinear elliptic optimal control problems”

POD error based inexact SQP method for bilinear elliptic optimal control problems

Martin Kahlbacher, Stefan Volkwein (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

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An optimal control problem governed by a bilinear elliptic equation is considered. This problem is solved by the sequential quadratic programming (SQP) method in an infinite-dimensional framework. In each level of this iterative method the solution of linear-quadratic subproblem is computed by a Galerkin projection using proper orthogonal decomposition (POD). Thus, an approximate (inexact) solution of the subproblem is determined. Based...

error estimates for a state-constrained elliptic optimal control problem

Arnd Rösch, Simeon Steinig (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

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We examine an elliptic optimal control problem with control and state constraints in ℝ. An improved error estimate of 𝒪( ) with 3/4 ≤ ≤ 1 − ε is proven for a discretisation involving piecewise constant functions for the control and piecewise linear for the state. The derived order of convergence is illustrated by a numerical example.

error estimates for a state-constrained elliptic optimal control problem

Arnd Rösch, Simeon Steinig (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

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We examine an elliptic optimal control problem with control and state constraints in ℝ. An improved error estimate of 𝒪( ) with 3/4 ≤ ≤ 1 − ε is proven for a discretisation involving piecewise constant functions for the control and piecewise linear for the state. The derived order of convergence is illustrated by a numerical example.

A priori error estimates for a state-constrained elliptic optimal control problem

Arnd Rösch, Simeon Steinig (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We examine an elliptic optimal control problem with control and state constraints in ℝ. An improved error estimate of 𝒪( ) with 3/4 ≤ ≤ 1 − ε is proven for a discretisation involving piecewise constant functions for the control and piecewise linear for the state. The derived order of convergence is illustrated by a numerical example.

A certified reduced basis method for parametrized elliptic optimal control problems

Mark Kärcher, Martin A. Grepl (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper, we employ the reduced basis method as a surrogate model for the solution of linear-quadratic optimal control problems governed by parametrized elliptic partial differential equations. We present error estimation and dual procedures that provide rigorous bounds for the error in several quantities of interest: the optimal control, the cost functional, and general linear output functionals of the control, state, and adjoint variables. We show that, based on the assumption...

New regularity results and improved error estimates for optimal control problems with state constraints

Eduardo Casas, Mariano Mateos, Boris Vexler (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we are concerned with a distributed optimal control problem governed by an elliptic partial differential equation. State constraints of box type are considered. We show that the Lagrange multiplier associated with the state constraints, which is known to be a measure, is indeed more regular under quite general assumptions. We discretize the problem by continuous piecewise linear finite elements and we are able to prove that, for the case of a linear equation, the order...

Error estimates for finite element approximations of elliptic control problems

Walter Alt, Nils Bräutigam, Arnd Rösch (2007)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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We investigate finite element approximations of one-dimensional elliptic control problems. For semidiscretizations and full discretizations with piecewise constant controls we derive error estimates in the maximum norm.

An error analysis of adaptive finite element methods for distributed elliptic control problems with control constraints

Michael Hintermüller, Ronald H.W. Hoppe, Yuri Iliash, Michael Kieweg (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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We present an error analysis of adaptive finite element approximations of distributed control problems for second order elliptic boundary value problems under bound constraints on the control. The error analysis is based on a residual-type error estimator that consists of edge and element residuals. Since we do not assume any regularity of the data of the problem, the error analysis further invokes data oscillations. We prove reliability and efficiency of the error estimator and provide...