Stable Methods for Ill-Posed Variational Problems: Prox-Regularization of Elliptic Variational Inequalities and Semi-Infinite Problems (Mathematical)

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ISBN 10: 3055016351 / ISBN 13: 9783055016356

Published by De Gruyter Akademie Forschung, 2014

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Zustand: Sehr gut | Seiten: 979 | Sprache: Englisch | Produktart: Bücher | Keine Beschreibung verfügbar.

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Bibliographic Details

• Title: Stable Methods for Ill-Posed Variational Problems: Prox-Regularization of Elliptic Variational Inequalities and Semi-Infinite Problems (Mathematical)
• Publisher: De Gruyter Akademie Forschung
• Publication Date: 2014
• Language: English
• ISBN 10: 3055016351
• ISBN 13: 9783055016356
• Binding: Hardcover
• Condition: Sehr gut
• Seller catalogs:
  • Bücher

About this title

Synopsis

Iterative prox-regularization methods for solving ill-posed convex variational problems in Hilbert spaces are subject of this book. A general framework is developed to analyse simultaneously procedures of regularization and successively refined discretization in connection with specific optimization methods for solving the discrete problems. This allows an efficient control of the solution process as a whole. In the first part of the book various methods for treating ill-posed problems are presented, including a study of the regularizing properties of a number of specific optimization algorithms. In the second part, a new class of multi-step methods is introduced which is based on a generalization of the iterative prox-regularization concept. Compared with former methods these new methods permit a more effective use of rough approximations of the infinite dimensional problems and consequently an acceleration of the numerical process. Special versions of these methods are given for ill-posed convex semi-infinite optimization problems and elliptic variational inequalities with weakly coercive operators, including some problems in elasticity theory.

From the Publisher

Applications to ill-posed variational problems in Hilbert spaces include elliptic inequalities from elasticity theory and semi-infinite programming.