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Passing to the Limit in Constrained Minimization Problems

  • Peter I. Kogut
  • Günter R. Leugering
Part of the Systems & Control: Foundations & Applications book series (SCFA)

Abstract

The main object of our consideration in this chapter is the following parameterized minimization problem
$$\left<\inf_{x\in\Xi_{\varepsilon}} I_{\varepsilon}(x)\right>,$$
where \(I_{{\varepsilon}}:(\Xi_{{\varepsilon}}\subseteq \mathbb{X}_{{\varepsilon}})\rightarrow\overline{\mathbb{R}}\) is an objective functional, \(\Xi_{{\varepsilon}}\subseteq \mathbb{X}_{{\varepsilon}}\) is a set of admissible solutions, and \(\mathbb{X}_{{\varepsilon}}\) is some Banach space.

Keywords

Banach Space Minimization Problem Variable Space Variational Limit Radon Measure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Faculty of Mathematics and Mechanics, Department of Differential EquationsOles Honchar Dnipropetrovsk National UniversityDnipropetrovskUkraine
  2. 2.Department of Mathematics, Chair of Applied Mathematics IIFriedrich-Alexander Universität Erlangen-NürnbergErlangenGermany

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