Passing to the Limit in Constrained Minimization Problems

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


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.


Banach Space Minimization Problem Variable Space Variational Limit Radon Measure 
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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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