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

Martin Kahlbacher, Stefan Volkwein (2012)

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

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 on a POD a-posteriori error estimator developed by Tröltzsch...

POD a-posteriori error based inexact SQP method for bilinear elliptic optimal control problems∗

Martin Kahlbacher, Stefan Volkwein (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

Projection iterative approximations for a new class of general random implicit quasi-variational inequalities.

Lan, Heng-You (2006)

Journal of Inequalities and Applications [electronic only]

Projection methods for retarded functional differential equations

H. Banks, Andrzej Manitius (1976)

Banach Center Publications

Properties of projection and penalty methods for discretized elliptic control problems

Andrzej Cegielski, Christian Grossmann (2007)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, properties of projection and penalty methods are studied in connection with control problems and their discretizations. In particular, the convergence of an interior-exterior penalty method applied to simple state constraints as well as the contraction behavior of projection mappings are analyzed. In this study, the focus is on the application of these methods to discretized control problem.