Optimization in Function Spaces : : With Stability Considerations in Orlicz Spaces / / Peter Kosmol, Dieter Müller-Wichards.
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 te...
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Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2011] ©2011 |
Year of Publication: | 2011 |
Language: | English |
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Physical Description: | 1 online resource (388 p.) |
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Kosmol, Peter, author. aut http://id.loc.gov/vocabulary/relators/aut Optimization in Function Spaces : With Stability Considerations in Orlicz Spaces / Peter Kosmol, Dieter Müller-Wichards. Berlin ; Boston : De Gruyter, [2011] ©2011 1 online resource (388 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda De Gruyter Series in Nonlinear Analysis and Applications , 0941-813X ; 13 Frontmatter -- Preface -- Contents -- 1 Approximation in Orlicz Spaces -- 2 Polya Algorithms in Orlicz Spaces -- 3 Convex Sets and Convex Functions -- 4 Numerical Treatment of Non-linear Equations and Optimization Problems -- 5 Stability and Two-stage Optimization Problems -- 6 Orlicz Spaces -- 7 Orlicz Norm and Duality -- 8 Differentiability and Convexity in Orlicz Spaces -- 9 Variational Calculus -- Bibliography -- List of Symbols -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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 Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 28. Feb 2023) Mathematical optimization. Orlicz spaces. Stability Mathematical models. Banach-Raum. Konvexe Optimierung. Orlicz-Raum. MATHEMATICS / Functional Analysis. bisacsh Banach space. Functional Analysis. Optimization. Orlicz space. Stability. Müller-Wichards, Dieter, author. aut http://id.loc.gov/vocabulary/relators/aut Title is part of eBook package: De Gruyter DG Studies in Nonlinear Analysis and Applications 9783110647099 Title is part of eBook package: De Gruyter DGBA Backlist Complete English Language 2000-2014 PART1 9783110238570 Title is part of eBook package: De Gruyter DGBA Backlist Mathematics 2000-2014 (EN) 9783110238471 Title is part of eBook package: De Gruyter DGBA Mathematics - 2000 - 2014 9783110637205 ZDB-23-GMA Title is part of eBook package: De Gruyter E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2010 9783110233544 ZDB-23-DGG Title is part of eBook package: De Gruyter E-BOOK PACKAGE ENGLISH LANGUAGES TITLES 2010 9783110233551 Title is part of eBook package: De Gruyter E-BOOK PAKET SCIENCE TECHNOLOGY AND MEDICINE 2010 9783110233636 ZDB-23-DMN print 9783110250206 https://doi.org/10.1515/9783110250213 https://www.degruyter.com/isbn/9783110250213 Cover https://www.degruyter.com/document/cover/isbn/9783110250213/original |
language |
English |
format |
eBook |
author |
Kosmol, Peter, Kosmol, Peter, Müller-Wichards, Dieter, |
spellingShingle |
Kosmol, Peter, Kosmol, Peter, Müller-Wichards, Dieter, Optimization in Function Spaces : With Stability Considerations in Orlicz Spaces / De Gruyter Series in Nonlinear Analysis and Applications , Frontmatter -- Preface -- Contents -- 1 Approximation in Orlicz Spaces -- 2 Polya Algorithms in Orlicz Spaces -- 3 Convex Sets and Convex Functions -- 4 Numerical Treatment of Non-linear Equations and Optimization Problems -- 5 Stability and Two-stage Optimization Problems -- 6 Orlicz Spaces -- 7 Orlicz Norm and Duality -- 8 Differentiability and Convexity in Orlicz Spaces -- 9 Variational Calculus -- Bibliography -- List of Symbols -- Index |
author_facet |
Kosmol, Peter, Kosmol, Peter, Müller-Wichards, Dieter, Müller-Wichards, Dieter, Müller-Wichards, Dieter, |
author_variant |
p k pk p k pk d m w dmw |
author_role |
VerfasserIn VerfasserIn VerfasserIn |
author2 |
Müller-Wichards, Dieter, Müller-Wichards, Dieter, |
author2_variant |
d m w dmw |
author2_role |
VerfasserIn VerfasserIn |
author_sort |
Kosmol, Peter, |
title |
Optimization in Function Spaces : With Stability Considerations in Orlicz Spaces / |
title_sub |
With Stability Considerations in Orlicz Spaces / |
title_full |
Optimization in Function Spaces : With Stability Considerations in Orlicz Spaces / Peter Kosmol, Dieter Müller-Wichards. |
title_fullStr |
Optimization in Function Spaces : With Stability Considerations in Orlicz Spaces / Peter Kosmol, Dieter Müller-Wichards. |
title_full_unstemmed |
Optimization in Function Spaces : With Stability Considerations in Orlicz Spaces / Peter Kosmol, Dieter Müller-Wichards. |
title_auth |
Optimization in Function Spaces : With Stability Considerations in Orlicz Spaces / |
title_alt |
Frontmatter -- Preface -- Contents -- 1 Approximation in Orlicz Spaces -- 2 Polya Algorithms in Orlicz Spaces -- 3 Convex Sets and Convex Functions -- 4 Numerical Treatment of Non-linear Equations and Optimization Problems -- 5 Stability and Two-stage Optimization Problems -- 6 Orlicz Spaces -- 7 Orlicz Norm and Duality -- 8 Differentiability and Convexity in Orlicz Spaces -- 9 Variational Calculus -- Bibliography -- List of Symbols -- Index |
title_new |
Optimization in Function Spaces : |
title_sort |
optimization in function spaces : with stability considerations in orlicz spaces / |
series |
De Gruyter Series in Nonlinear Analysis and Applications , |
series2 |
De Gruyter Series in Nonlinear Analysis and Applications , |
publisher |
De Gruyter, |
publishDate |
2011 |
physical |
1 online resource (388 p.) Issued also in print. |
contents |
Frontmatter -- Preface -- Contents -- 1 Approximation in Orlicz Spaces -- 2 Polya Algorithms in Orlicz Spaces -- 3 Convex Sets and Convex Functions -- 4 Numerical Treatment of Non-linear Equations and Optimization Problems -- 5 Stability and Two-stage Optimization Problems -- 6 Orlicz Spaces -- 7 Orlicz Norm and Duality -- 8 Differentiability and Convexity in Orlicz Spaces -- 9 Variational Calculus -- Bibliography -- List of Symbols -- Index |
isbn |
9783110250213 9783110647099 9783110238570 9783110238471 9783110637205 9783110233544 9783110233551 9783110233636 9783110250206 |
issn |
0941-813X ; |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA871 |
callnumber-sort |
QA 3871 K8235 42011EB |
url |
https://doi.org/10.1515/9783110250213 https://www.degruyter.com/isbn/9783110250213 https://www.degruyter.com/document/cover/isbn/9783110250213/original |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
515 - Analysis |
dewey-full |
515/.392 |
dewey-sort |
3515 3392 |
dewey-raw |
515/.392 |
dewey-search |
515/.392 |
doi_str_mv |
10.1515/9783110250213 |
oclc_num |
754713662 |
work_keys_str_mv |
AT kosmolpeter optimizationinfunctionspaceswithstabilityconsiderationsinorliczspaces AT mullerwichardsdieter optimizationinfunctionspaceswithstabilityconsiderationsinorliczspaces |
status_str |
n |
ids_txt_mv |
(DE-B1597)114002 (OCoLC)754713662 |
carrierType_str_mv |
cr |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter DG Studies in Nonlinear Analysis and Applications Title is part of eBook package: De Gruyter DGBA Backlist Complete English Language 2000-2014 PART1 Title is part of eBook package: De Gruyter DGBA Backlist Mathematics 2000-2014 (EN) Title is part of eBook package: De Gruyter DGBA Mathematics - 2000 - 2014 Title is part of eBook package: De Gruyter E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2010 Title is part of eBook package: De Gruyter E-BOOK PACKAGE ENGLISH LANGUAGES TITLES 2010 Title is part of eBook package: De Gruyter E-BOOK PAKET SCIENCE TECHNOLOGY AND MEDICINE 2010 |
is_hierarchy_title |
Optimization in Function Spaces : With Stability Considerations in Orlicz Spaces / |
container_title |
Title is part of eBook package: De Gruyter DG Studies in Nonlinear Analysis and Applications |
author2_original_writing_str_mv |
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