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110721 r ||| eng |
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|a 9783110250213
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|a QA871
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| 100 |
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|a Kosmol, Peter
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| 245 |
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|a Optimization in Function Spaces
|h Elektronische Ressource
|b With Stability Considerations in Orlicz Spaces
|c Peter Kosmol, Dieter Müller-Wichards
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| 260 |
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|a Berlin
|b De Gruyter
|c [2011]©2011, 2011
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| 300 |
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|a 402 p.
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| 653 |
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|a MATHEMATICS / Functional Analysis / bisacsh
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| 653 |
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|a Konvexe Optimierung
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| 653 |
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|a Banach-Raum
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| 653 |
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|a (DE-601)10415215X / (DE-588)4056693-6 / Stabilität / gnd
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| 653 |
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|a Orlicz-Raum
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| 653 |
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|a Orlicz space
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| 653 |
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|a Stability
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| 653 |
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|a Optimization
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| 653 |
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|a Stability / Mathematical models
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| 653 |
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|a Functional Analysis
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| 653 |
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|a (DE-601)104603658 / (DE-588)4004402-6 / Banach-Raum / gnd
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| 653 |
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|a Orlicz spaces
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| 653 |
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|a Banach space
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| 653 |
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|a (DE-601)105384410 / (DE-588)4172841-5 / Orlicz-Raum / gnd
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| 653 |
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|a Mathematical optimization
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| 653 |
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|a (DE-601)105653101 / (DE-588)4137027-2 / Konvexe Optimierung / gnd
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| 700 |
1 |
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|a Müller-Wichards, Dieter
|e [author]
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| 041 |
0 |
7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b GRUYMPG
|a DeGruyter MPG Collection
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| 490 |
0 |
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|a De Gruyter Series in Nonlinear Analysis and Applications
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| 500 |
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|a Mode of access: Internet via World Wide Web
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| 028 |
5 |
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|a 10.1515/9783110250213
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| 773 |
0 |
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|t DGBA Backlist Mathematics English Language 2000-2014
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| 773 |
0 |
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|t DGBA Backlist Complete English Language 2000-2014 PART1
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| 773 |
0 |
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|t DGBA Mathematics 2000 - 2014
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| 773 |
0 |
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|t E-BOOK PAKET SCIENCE TECHNOLOGY AND MEDICINE 2010
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| 773 |
0 |
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|t E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2010
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| 773 |
0 |
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|t E-BOOK PACKAGE ENGLISH LANGUAGES TITLES 2010
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| 856 |
4 |
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|u https://www.degruyter.com/doi/book/10.1515/9783110250213?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
0 |
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|a 515.392
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| 520 |
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|a 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
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