Application of the augmented Lagrangian-SQP method to optimal control problems for the stationary Burgers equation
type: Item
instance of: scholarly article
title: Application of the augmented Lagrangian-SQP method to optimal control problems for the stationary Burgers equation
zbMATH Open document ID: 0974.49020
DOI: 10.1023/A:1008777520259
published in: Computational Optimization and Applications
publication date: 2001-01-22T00:00:00Z
review text: This paper discusses the application of the augmented Lagrangian-sequential quadratic programming (SQP) method to optimal control problems with least squares objective function which are governed by the stationary viscous Burgers equation. Section 2 reviews local convergence properties of the augmented Lagrangian-SQP method in Hilbert space. Sections 3 and 4 are concerned with distributed and Neumann boundary control problems, respectively. Existence of a solution to the optimal control problems are proven, first order necessary optimality conditions are established, and second order sufficient optimality conditions are shown under the assumption that the least squares residual at the solution is sufficiently small (in case of a Neumann boundary control and \(L^2\) observations one also needs a condition on the viscosity parameter). In the final section, a finite element discretization using piecewise linear elements is discussed. Mesh independent convergence of the augmented Lagrangian-SQP method is proven and demonstrated numerically.
Mathematics Subject Classification ID: 49M37
Mathematics Subject Classification ID: 90C55
Mathematics Subject Classification ID: 49K20
Mathematics Subject Classification ID: 35Q53
zbMATH DE Number: 1499059
zbMATH Keywords: augmented Lagrangian method
zbMATH Keywords: sequential quadratic programming method
zbMATH Keywords: optimal control problems
zbMATH Keywords: Burgers equation
zbMATH Keywords: mesh independence
author: S. Volkwein
reviewed by: M. Heinkenschloss
MaRDI profile type: Publication
full work available at URL: a:1008777520259
OpenAlex ID: W180711869
description: scientific article; zbMATH DE number 1499059