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Penalties, Lagrange multipliers and Nitsche mortaring

100%
Grossmann C.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2010
|
tom 30
|
nr 2
205-220
EN
Penalty methods, augmented Lagrangian methods and Nitsche mortaring are well known numerical methods among the specialists in the related areas optimization and finite elements, respectively, but common aspects are rarely available. The aim of the present paper is to describe these methods from a unifying optimization perspective and to highlight some common features of them.
2
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Penalty/barrier path-following in linearly constrained optimization

100%
Grossmann C.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2000
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tom 20
|
nr 1
7-26
EN
In the present paper rather general penalty/barrier path-following methods (e.g. with p-th power penalties, logarithmic barriers, SUMT, exponential penalties) applied to linearly constrained convex optimization problems are studied. In particular, unlike in previous studies [1,11], here simultaneously different types of penalty/barrier embeddings are included. Together with the assumed 2nd order sufficient optimality conditions this required a significant change in proving the local existence of some continuously differentiable primal and dual path related to these methods. In contrast to standard penalty/barrier investigations in the considered path-following algorithms only one Newton step is applied to the generated auxiliary problems. As a foundation of convergence analysis the radius of convergence of Newton's method depending on the penalty/barrier parameter is estimated. There are established parameter selection rules which guarantee the overall convergence of the considered path-following penalty/barrier techniques.
3
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Properties of projection and penalty methods for discretized elliptic control problems

63%
Cegielski A., Grossmann C.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2007
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tom 27
|
nr 1
23-41
EN
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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