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This is an essentially self-contained book on the theory of convex functions and convex optimization in Banach spaces, with a special interest in Orlicz spaces.
Approximate algorithms based on the stability principles and the solution of the corresponding nonlinear equations are developed in this text. A synopsis of the geometry of Banach spaces, aspects of stability and the duality of different levels of differentiability and convexity is developed. A particular emphasis is placed on the geometrical aspects of strong solvability of a convex optimization problem: it turns out that this property is equivalent to local uniform convexity of the corresponding convex function. This treatise also provides a novel approach to the fundamental theorems of Variational Calculus based on the principle of pointwise minimization of the Lagrangian on the one hand and convexification by quadratic supplements using the classical Legendre-Ricatti equation on the other.
The reader should be familiar with the concepts of mathematical analysis and linear algebra. Some awareness of the principles of measure theory will turn out to be helpful. The book is suitable for students of the second half of undergraduate studies, and it provides a rich set of material for a master course on linear and nonlinear functional analysis. Additionally it offers novel aspects at the advanced level.
From the contents:
- Approximation and Polya Algorithms in Orlicz Spaces
- Convex Sets and Convex Functions
- Numerical Treatment of Non-linear Equations and Optimization Problems
- Stability and Two-stage Optimization Problems
- Orlicz Spaces, Orlicz Norm and Duality
- Differentiability and Convexity in Orlicz Spaces
- Variational Calculus
Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.
Informazioni sull?autore
Peter Kosmol, Christian Albrechts University, Kiel, Germany; Dieter Müller-Wichards, Hamburg University of Applied Sciences, Germany.
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Optimization in Function Spaces With Stability Considerations in Orlicz Spaces
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Walter de Gruyter, Incorporated, 2011
ISBN 10: 3110250209
ISBN 13: 9783110250206
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Optimization in Function Spaces With Stability Considerations in Orlicz Spaces
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Walter de Gruyter, Incorporated, 2011
ISBN 10: 3110250209
ISBN 13: 9783110250206
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Optimization In Function Spaces With Stability Considerations In Orlicz Spaces
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OPTIMIZATION IN FUNCTION SPACES: WITH STABILITY CONSIDERATIONS IN ORLICZ SPACES (13) (HB)
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Optimization in Function Spaces : With Stability Considerations in Orlicz Spaces
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Buch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - This is an essentially self-contained book on the theory of convex functions and convex optimization in Banach spaces, with a special interest in Orlicz spaces. Approximate algorithms based on the stability principles and the solution of the corresponding nonlinear equations are developed in this text. A synopsis of the geometry of Banach spaces, aspects of stability and the duality of different levels of differentiability and convexity is developed. A particular emphasis is placed on the geometrical aspects of strong solvability of a convex optimization problem: it turns out that this property is equivalent to local uniform convexity of the corresponding convex function. This treatise also provides a novel approach to the fundamental theorems of Variational Calculus based on the principle of pointwise minimization of the Lagrangian on the one hand and convexification by quadratic supplements using the classical Legendre-Ricatti equation on the other. The reader should be familiar with the concepts of mathematical analysis and linear algebra. Some awareness of the principles of measure theory will turn out to be helpful. The book is suitable for students of the second half of undergraduate studies, and it provides a rich set of material for a master course on linear and nonlinear functional analysis. Additionally it offers novel aspects at the advanced level. From the contents: Approximation and Polya Algorithms in Orlicz Spaces Convex Sets and Convex Functions Numerical Treatment of Non-linear Equations and Optimization Problems Stability and Two-stage Optimization Problems Orlicz Spaces, Orlicz Norm and Duality Differentiability and Convexity in Orlicz Spaces Variational Calculus. Codice articolo 9783110250206
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Optimization in Function Spaces
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De Gruyter, De Gruyter Feb 2011, 2011
ISBN 10: 3110250209
ISBN 13: 9783110250206
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Buch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. Neuware -This is an essentially self-contained book on the theory of convex functions and convex optimization in Banach spaces, with a special interest in Orlicz spaces.Approximate algorithms based on the stability principles and the solution of the corresponding nonlinear equations are developed in this text. A synopsis of the geometry of Banach spaces, aspects of stability and the duality of different levels of differentiability and convexity is developed. A particular emphasis is placed on the geometrical aspects of strong solvability of a convex optimization problem: it turns out that this property is equivalent to local uniform convexity of the corresponding convex function. This treatise also provides a novel approach to the fundamental theorems of Variational Calculus based on the principle of pointwise minimization of the Lagrangian on the one hand and convexification by quadratic supplements using the classical Legendre-Ricatti equation on the other.The reader should be familiar with the concepts of mathematical analysis and linear algebra. Some awareness of the principles of measure theory will turn out to be helpful. The book is suitable for students of the second half of undergraduate studies, and it provides a rich set of material for a master course on linear and nonlinear functional analysis. Additionally it offers novel aspects at the advanced level.From the contents: Approximation and Polya Algorithms in Orlicz SpacesConvex Sets and Convex FunctionsNumerical Treatment of Non-linear Equations and Optimization ProblemsStability and Two-stage Optimization ProblemsOrlicz Spaces, Orlicz Norm and DualityDifferentiability and Convexity in Orlicz SpacesVariational CalculusWalter de Gruyter GmbH, Genthiner Strasse 13, 10785 Berlin 404 pp. Englisch. Codice articolo 9783110250206
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Optimization in Function Spaces: With Stability Considerations in Orlicz Spaces (De Gruyter Series in Nonlinear Analysis and Applications, 13)
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Optimization in Function Spaces With Stability Considerations in Orlicz Spaces de Gruyter Series In Nonlinear Analysis And Applications 13 De in Nonlinear Analysis Applications, 13
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Optimization in Function Spaces
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