Optimization in function spaces :: with stability considerations in Orlicz spaces /
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...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; New York :
De Gruyter,
2011.
|
| Schriftenreihe: | De Gruyter series in nonlinear analysis and applications ;
13. |
| Schlagworte: | |
| Online-Zugang: | DE-862 DE-863 |
| Zusammenfassung: | 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. And it is provided 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. |
| Beschreibung: | 1 online resource (xiv, 388 pages) : illustrations |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9783110250213 3110250217 1283166348 9781283166348 3110250209 9783110250206 |
| ISSN: | 0941-813X ; |
Internformat
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| 100 | 1 | |a Kosmol, Peter. | |
| 245 | 1 | 0 | |a Optimization in function spaces : |b with stability considerations in Orlicz spaces / |c Peter Kosmol, Dieter Müller-Wichards. |
| 260 | |a Berlin ; |a New York : |b De Gruyter, |c 2011. | ||
| 300 | |a 1 online resource (xiv, 388 pages) : |b illustrations | ||
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| 490 | 1 | |a De Gruyter series in nonlinear analysis and applications, |x 0941-813X ; |v 13 | |
| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |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. And it is provided 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. | ||
| 505 | 0 | |a 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. | |
| 650 | 0 | |a Stability |x Mathematical models. | |
| 650 | 0 | |a Mathematical optimization. |0 http://id.loc.gov/authorities/subjects/sh85082127 | |
| 650 | 0 | |a Orlicz spaces. |0 http://id.loc.gov/authorities/subjects/sh85095692 | |
| 650 | 6 | |a Stabilité |x Modèles mathématiques. | |
| 650 | 6 | |a Optimisation mathématique. | |
| 650 | 6 | |a Espaces d'Orlicz. | |
| 650 | 7 | |a MATHEMATICS |x Differential Equations |x General. |2 bisacsh | |
| 650 | 7 | |a Mathematical optimization |2 fast | |
| 650 | 7 | |a Orlicz spaces |2 fast | |
| 650 | 7 | |a Stability |x Mathematical models |2 fast | |
| 650 | 7 | |a Stabilität |2 gnd |0 http://d-nb.info/gnd/4056693-6 | |
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| 650 | 7 | |a Konvexe Optimierung |2 gnd |0 http://d-nb.info/gnd/4137027-2 | |
| 653 | |a Banach space. | ||
| 653 | |a Functional Analysis. | ||
| 653 | |a Optimization. | ||
| 653 | |a Orlicz space. | ||
| 653 | |a Stability. | ||
| 655 | 0 | |a Electronic books. | |
| 700 | 1 | |a Müller-Wichards, D. |q (Dieter), |d 1946- |1 https://id.oclc.org/worldcat/entity/E39PBJtcBtmKmhJJVGMckj4wmd |0 http://id.loc.gov/authorities/names/n88117691 | |
| 776 | 0 | 8 | |i Print version: |a Kosmol, Peter. |t Optimization in function spaces. |d Berlin ; New York : De Gruyter, 2011 |w (DLC) 2010036123 |
| 830 | 0 | |a De Gruyter series in nonlinear analysis and applications ; |v 13. |x 0941-813X |0 http://id.loc.gov/authorities/names/n92047842 | |
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Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn754713662 |
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| _version_ | 1829094705936203776 |
| adam_text | |
| any_adam_object | |
| author | Kosmol, Peter |
| author2 | Müller-Wichards, D. (Dieter), 1946- |
| author2_role | |
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| author_GND | http://id.loc.gov/authorities/names/n88117691 |
| author_facet | Kosmol, Peter Müller-Wichards, D. (Dieter), 1946- |
| author_role | |
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| callnumber-subject | QA - Mathematics |
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| collection | ZDB-4-EBA |
| contents | 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. |
| ctrlnum | (OCoLC)754713662 |
| dewey-full | 515/.392 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.392 |
| dewey-search | 515/.392 |
| dewey-sort | 3515 3392 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| genre | Electronic books. |
| genre_facet | Electronic books. |
| id | ZDB-4-EBA-ocn754713662 |
| illustrated | Illustrated |
| indexdate | 2025-04-11T08:37:23Z |
| institution | BVB |
| isbn | 9783110250213 3110250217 1283166348 9781283166348 3110250209 9783110250206 |
| issn | 0941-813X ; |
| language | English |
| oclc_num | 754713662 |
| open_access_boolean | |
| owner | MAIN DE-862 DE-BY-FWS DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-862 DE-BY-FWS DE-863 DE-BY-FWS |
| physical | 1 online resource (xiv, 388 pages) : illustrations |
| psigel | ZDB-4-EBA FWS_PDA_EBA ZDB-4-EBA |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | De Gruyter, |
| record_format | marc |
| series | De Gruyter series in nonlinear analysis and applications ; |
| series2 | De Gruyter series in nonlinear analysis and applications, |
| spelling | Kosmol, Peter. Optimization in function spaces : with stability considerations in Orlicz spaces / Peter Kosmol, Dieter Müller-Wichards. Berlin ; New York : De Gruyter, 2011. 1 online resource (xiv, 388 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier De Gruyter series in nonlinear analysis and applications, 0941-813X ; 13 Includes bibliographical references and index. Print version record. 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. And it is provided 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. 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. Stability Mathematical models. Mathematical optimization. http://id.loc.gov/authorities/subjects/sh85082127 Orlicz spaces. http://id.loc.gov/authorities/subjects/sh85095692 Stabilité Modèles mathématiques. Optimisation mathématique. Espaces d'Orlicz. MATHEMATICS Differential Equations General. bisacsh Mathematical optimization fast Orlicz spaces fast Stability Mathematical models fast Stabilität gnd http://d-nb.info/gnd/4056693-6 Banach-Raum gnd http://d-nb.info/gnd/4004402-6 Orlicz-Raum gnd http://d-nb.info/gnd/4172841-5 Konvexe Optimierung gnd http://d-nb.info/gnd/4137027-2 Banach space. Functional Analysis. Optimization. Orlicz space. Stability. Electronic books. Müller-Wichards, D. (Dieter), 1946- https://id.oclc.org/worldcat/entity/E39PBJtcBtmKmhJJVGMckj4wmd http://id.loc.gov/authorities/names/n88117691 Print version: Kosmol, Peter. Optimization in function spaces. Berlin ; New York : De Gruyter, 2011 (DLC) 2010036123 De Gruyter series in nonlinear analysis and applications ; 13. 0941-813X http://id.loc.gov/authorities/names/n92047842 |
| spellingShingle | Kosmol, Peter Optimization in function spaces : with stability considerations in Orlicz spaces / De Gruyter series in nonlinear analysis and applications ; 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. Stability Mathematical models. Mathematical optimization. http://id.loc.gov/authorities/subjects/sh85082127 Orlicz spaces. http://id.loc.gov/authorities/subjects/sh85095692 Stabilité Modèles mathématiques. Optimisation mathématique. Espaces d'Orlicz. MATHEMATICS Differential Equations General. bisacsh Mathematical optimization fast Orlicz spaces fast Stability Mathematical models fast Stabilität gnd http://d-nb.info/gnd/4056693-6 Banach-Raum gnd http://d-nb.info/gnd/4004402-6 Orlicz-Raum gnd http://d-nb.info/gnd/4172841-5 Konvexe Optimierung gnd http://d-nb.info/gnd/4137027-2 |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85082127 http://id.loc.gov/authorities/subjects/sh85095692 http://d-nb.info/gnd/4056693-6 http://d-nb.info/gnd/4004402-6 http://d-nb.info/gnd/4172841-5 http://d-nb.info/gnd/4137027-2 |
| title | Optimization in function spaces : with stability considerations in Orlicz spaces / |
| title_auth | Optimization in function spaces : with stability considerations in Orlicz spaces / |
| title_exact_search | Optimization in function spaces : 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_short | Optimization in function spaces : |
| title_sort | optimization in function spaces with stability considerations in orlicz spaces |
| title_sub | with stability considerations in Orlicz spaces / |
| topic | Stability Mathematical models. Mathematical optimization. http://id.loc.gov/authorities/subjects/sh85082127 Orlicz spaces. http://id.loc.gov/authorities/subjects/sh85095692 Stabilité Modèles mathématiques. Optimisation mathématique. Espaces d'Orlicz. MATHEMATICS Differential Equations General. bisacsh Mathematical optimization fast Orlicz spaces fast Stability Mathematical models fast Stabilität gnd http://d-nb.info/gnd/4056693-6 Banach-Raum gnd http://d-nb.info/gnd/4004402-6 Orlicz-Raum gnd http://d-nb.info/gnd/4172841-5 Konvexe Optimierung gnd http://d-nb.info/gnd/4137027-2 |
| topic_facet | Stability Mathematical models. Mathematical optimization. Orlicz spaces. Stabilité Modèles mathématiques. Optimisation mathématique. Espaces d'Orlicz. MATHEMATICS Differential Equations General. Mathematical optimization Orlicz spaces Stability Mathematical models Stabilität Banach-Raum Orlicz-Raum Konvexe Optimierung Electronic books. |
| work_keys_str_mv | AT kosmolpeter optimizationinfunctionspaceswithstabilityconsiderationsinorliczspaces AT mullerwichardsd optimizationinfunctionspaceswithstabilityconsiderationsinorliczspaces |