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Projection method with level control in convex minimization

Robert Dylewski (2010)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We study a projection method with level control for nonsmoooth convex minimization problems. We introduce a changeable level parameter to level control. The level estimates the minimal value of the objective function and is updated in each iteration. We analyse the convergence and estimate the efficiency of this method.

Proper orthogonal decomposition for optimality systems

Karl Kunisch, Stefan Volkwein (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

Proper orthogonal decomposition (POD) is a powerful technique for model reduction of non-linear systems. It is based on a Galerkin type discretization with basis elements created from the dynamical system itself. In the context of optimal control this approach may suffer from the fact that the basis elements are computed from a reference trajectory containing features which are quite different from those of the optimally controlled trajectory. A method is proposed which avoids this problem of unmodelled...

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.

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