UID:
almahu_9949462115402882
Umfang:
1 online resource (388 p.)
ISBN:
9783110250213
,
9783110647099
Serie:
De Gruyter Series in Nonlinear Analysis and Applications , 13
Inhalt:
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
Anmerkung:
Frontmatter --
,
Preface --
,
Contents --
,
1 Approximation in Orlicz Spaces --
,
2 Polya Algorithms in Orlicz Spaces --
,
3 Convex Sets and Convex Functions --
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4 Numerical Treatment of Non-linear Equations and Optimization Problems --
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5 Stability and Two-stage Optimization Problems --
,
6 Orlicz Spaces --
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7 Orlicz Norm and Duality --
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8 Differentiability and Convexity in Orlicz Spaces --
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9 Variational Calculus --
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Bibliography --
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List of Symbols --
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Index
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Issued also in print.
,
Mode of access: Internet via World Wide Web.
,
In English.
In:
DG Studies in Nonlinear Analysis and Applications, De Gruyter, 9783110647099
In:
DGBA Backlist Complete English Language 2000-2014 PART1, De Gruyter, 9783110238570
In:
DGBA Backlist Mathematics 2000-2014 (EN), De Gruyter, 9783110238471
In:
DGBA Mathematics - 2000 - 2014, De Gruyter, 9783110637205
In:
E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2010, De Gruyter, 9783110233544
In:
E-BOOK PACKAGE ENGLISH LANGUAGES TITLES 2010, De Gruyter, 9783110233551
In:
E-BOOK PAKET SCIENCE TECHNOLOGY AND MEDICINE 2010, De Gruyter, 9783110233636
Weitere Ausg.:
ISBN 9783110250206
Sprache:
Englisch
Fachgebiete:
Mathematik
DOI:
10.1515/9783110250213
URL:
https://doi.org/10.1515/9783110250213
URL:
https://www.degruyter.com/isbn/9783110250213
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