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

Kaplan, Alexander; Tichatschke, Rainer

Hardcover

ISBN 10: 3055016351 ISBN 13: 9783055016356

Publisher: Wiley-VCH, 1994

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.

About this title

From the Publisher

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

About the Author

Martin Schneider, Herma Kliege-Biller und Stefan Meier-Oeser, Leibniz-Forschungsstelle, University of Munster, Germany."

Edition details

• Publisher: Wiley-VCH
• Publication date: 1994
• Language: English
• ISBN 10: 3055016351
• ISBN 13: 9783055016356
• Binding: Hardcover
• Edition number: 1
• Number of pages: 438