Convex analysis in general vector spaces /:
Annotation The primary aim of this book is to present the conjugate and sub/differential calculus using the method of perturbation functions in order to obtain the most general results in this field. The secondary aim is to provide important applications of this calculus and of the properties of con...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
River Edge, N.J. ; London :
World Scientific,
©2002.
|
| Schlagworte: | |
| Online-Zugang: | DE-862 DE-863 |
| Zusammenfassung: | Annotation The primary aim of this book is to present the conjugate and sub/differential calculus using the method of perturbation functions in order to obtain the most general results in this field. The secondary aim is to provide important applications of this calculus and of the properties of convex functions. Such applications are: the study of well-conditioned convex functions, uniformly convex and uniformly smooth convex functions, best approximation problems, characterizations of convexity, the study of the sets of weak sharp minima, well-behaved functions and the existence of global error bounds for convex inequalities, as well as the study of monotone multifunctions by using convex functions. |
| Beschreibung: | 1 online resource (xx, 367 pages) |
| Bibliographie: | Includes bibliographical references (pages 349-357) and index. |
| ISBN: | 9789812777096 9812777091 |
Internformat
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| 245 | 1 | 0 | |a Convex analysis in general vector spaces / |c C Zălinescu. |
| 260 | |a River Edge, N.J. ; |a London : |b World Scientific, |c ©2002. | ||
| 300 | |a 1 online resource (xx, 367 pages) | ||
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| 504 | |a Includes bibliographical references (pages 349-357) and index. | ||
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| 520 | 8 | |a Annotation The primary aim of this book is to present the conjugate and sub/differential calculus using the method of perturbation functions in order to obtain the most general results in this field. The secondary aim is to provide important applications of this calculus and of the properties of convex functions. Such applications are: the study of well-conditioned convex functions, uniformly convex and uniformly smooth convex functions, best approximation problems, characterizations of convexity, the study of the sets of weak sharp minima, well-behaved functions and the existence of global error bounds for convex inequalities, as well as the study of monotone multifunctions by using convex functions. | |
| 505 | 0 | |a Ch. 1. Preliminary results on functional analysis. 1.1. Preliminary notions and results. 1.2. Closedness and interiority notions. 1.3. Open mapping theorems. 1.4. Variational principles. 1.5. Exercises. 1.6. Bibliographical notes -- ch. 2. Convex analysis in locally convex spaces. 2.1. Convex functions. 2.2. Semi-continuity of convex functions. 2.3. Conjugate functions. 2.4. The subdifferential of a convex function. 2.5. The general problem of convex programming. 2.6. Perturbed problems. 2.7. The fundamental duality formula. 2.8. Formulas for conjugates and e-subdifferentials, duality relations and optimality conditions. 2.9. Convex optimization with constraints. 2.10. A minimax theorem. 2.11. Exercises. 2.12. Bibliographical notes -- ch. 3. Some results and applications of convex analysis in normed spaces. 3.1. Further fundamental results in convex analysis. 3.2. Convexity and monotonicity of subdifferentials. 3.3. Some classes of functions of a real variable and differentiability of convex functions. 3.4. Well conditioned functions. 3.5. Uniformly convex and uniformly smooth convex functions. 3.6. Uniformly convex and uniformly smooth convex functions on bounded sets. 3.7. Applications to the geometry of normed spaces. 3.8. Applications to the best approximation problem. 3.9. Characterizations of convexity in terms of smoothness. 3.10. Weak sharp minima, well-behaved functions and global error bounds for convex inequalities. 3.11. Monotone multifunctions. 3.12. Exercises. 3.13. Bibliographical notes. | |
| 546 | |a English. | ||
| 650 | 0 | |a Convex functions. |0 http://id.loc.gov/authorities/subjects/sh85031728 | |
| 650 | 0 | |a Convex sets. |0 http://id.loc.gov/authorities/subjects/sh85031731 | |
| 650 | 0 | |a Functional analysis. |0 http://id.loc.gov/authorities/subjects/sh85052312 | |
| 650 | 0 | |a Vector spaces. |0 http://id.loc.gov/authorities/subjects/sh85142456 | |
| 650 | 6 | |a Fonctions convexes. | |
| 650 | 6 | |a Ensembles convexes. | |
| 650 | 6 | |a Analyse fonctionnelle. | |
| 650 | 6 | |a Espaces vectoriels. | |
| 650 | 7 | |a MATHEMATICS |x Calculus. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Mathematical Analysis. |2 bisacsh | |
| 650 | 7 | |a Convex functions |2 fast | |
| 650 | 7 | |a Convex sets |2 fast | |
| 650 | 7 | |a Functional analysis |2 fast | |
| 650 | 7 | |a Vector spaces |2 fast | |
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| author | Zalinescu, C., 1952- |
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| contents | Ch. 1. Preliminary results on functional analysis. 1.1. Preliminary notions and results. 1.2. Closedness and interiority notions. 1.3. Open mapping theorems. 1.4. Variational principles. 1.5. Exercises. 1.6. Bibliographical notes -- ch. 2. Convex analysis in locally convex spaces. 2.1. Convex functions. 2.2. Semi-continuity of convex functions. 2.3. Conjugate functions. 2.4. The subdifferential of a convex function. 2.5. The general problem of convex programming. 2.6. Perturbed problems. 2.7. The fundamental duality formula. 2.8. Formulas for conjugates and e-subdifferentials, duality relations and optimality conditions. 2.9. Convex optimization with constraints. 2.10. A minimax theorem. 2.11. Exercises. 2.12. Bibliographical notes -- ch. 3. Some results and applications of convex analysis in normed spaces. 3.1. Further fundamental results in convex analysis. 3.2. Convexity and monotonicity of subdifferentials. 3.3. Some classes of functions of a real variable and differentiability of convex functions. 3.4. Well conditioned functions. 3.5. Uniformly convex and uniformly smooth convex functions. 3.6. Uniformly convex and uniformly smooth convex functions on bounded sets. 3.7. Applications to the geometry of normed spaces. 3.8. Applications to the best approximation problem. 3.9. Characterizations of convexity in terms of smoothness. 3.10. Weak sharp minima, well-behaved functions and global error bounds for convex inequalities. 3.11. Monotone multifunctions. 3.12. Exercises. 3.13. Bibliographical notes. |
| ctrlnum | (OCoLC)285163112 |
| dewey-full | 515/.8 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.8 |
| dewey-search | 515/.8 |
| dewey-sort | 3515 18 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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The secondary aim is to provide important applications of this calculus and of the properties of convex functions. Such applications are: the study of well-conditioned convex functions, uniformly convex and uniformly smooth convex functions, best approximation problems, characterizations of convexity, the study of the sets of weak sharp minima, well-behaved functions and the existence of global error bounds for convex inequalities, as well as the study of monotone multifunctions by using convex functions.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Ch. 1. Preliminary results on functional analysis. 1.1. Preliminary notions and results. 1.2. Closedness and interiority notions. 1.3. Open mapping theorems. 1.4. Variational principles. 1.5. Exercises. 1.6. Bibliographical notes -- ch. 2. Convex analysis in locally convex spaces. 2.1. Convex functions. 2.2. Semi-continuity of convex functions. 2.3. Conjugate functions. 2.4. The subdifferential of a convex function. 2.5. The general problem of convex programming. 2.6. Perturbed problems. 2.7. The fundamental duality formula. 2.8. Formulas for conjugates and e-subdifferentials, duality relations and optimality conditions. 2.9. Convex optimization with constraints. 2.10. A minimax theorem. 2.11. Exercises. 2.12. Bibliographical notes -- ch. 3. Some results and applications of convex analysis in normed spaces. 3.1. Further fundamental results in convex analysis. 3.2. Convexity and monotonicity of subdifferentials. 3.3. Some classes of functions of a real variable and differentiability of convex functions. 3.4. Well conditioned functions. 3.5. Uniformly convex and uniformly smooth convex functions. 3.6. Uniformly convex and uniformly smooth convex functions on bounded sets. 3.7. Applications to the geometry of normed spaces. 3.8. Applications to the best approximation problem. 3.9. Characterizations of convexity in terms of smoothness. 3.10. Weak sharp minima, well-behaved functions and global error bounds for convex inequalities. 3.11. Monotone multifunctions. 3.12. Exercises. 3.13. 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| id | ZDB-4-EBA-ocn285163112 |
| illustrated | Not Illustrated |
| indexdate | 2025-03-18T14:14:38Z |
| institution | BVB |
| isbn | 9789812777096 9812777091 |
| language | English |
| oclc_num | 285163112 |
| open_access_boolean | |
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| owner_facet | MAIN DE-862 DE-BY-FWS DE-863 DE-BY-FWS |
| physical | 1 online resource (xx, 367 pages) |
| psigel | ZDB-4-EBA FWS_PDA_EBA ZDB-4-EBA |
| publishDate | 2002 |
| publishDateSearch | 2002 |
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| publisher | World Scientific, |
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| spelling | Zalinescu, C., 1952- https://id.oclc.org/worldcat/entity/E39PBJdx9ymT4mRFpyGQyt3CwC http://id.loc.gov/authorities/names/n2002014033 Convex analysis in general vector spaces / C Zălinescu. River Edge, N.J. ; London : World Scientific, ©2002. 1 online resource (xx, 367 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier data file Includes bibliographical references (pages 349-357) and index. Print version record. Annotation The primary aim of this book is to present the conjugate and sub/differential calculus using the method of perturbation functions in order to obtain the most general results in this field. The secondary aim is to provide important applications of this calculus and of the properties of convex functions. Such applications are: the study of well-conditioned convex functions, uniformly convex and uniformly smooth convex functions, best approximation problems, characterizations of convexity, the study of the sets of weak sharp minima, well-behaved functions and the existence of global error bounds for convex inequalities, as well as the study of monotone multifunctions by using convex functions. Ch. 1. Preliminary results on functional analysis. 1.1. Preliminary notions and results. 1.2. Closedness and interiority notions. 1.3. Open mapping theorems. 1.4. Variational principles. 1.5. Exercises. 1.6. Bibliographical notes -- ch. 2. Convex analysis in locally convex spaces. 2.1. Convex functions. 2.2. Semi-continuity of convex functions. 2.3. Conjugate functions. 2.4. The subdifferential of a convex function. 2.5. The general problem of convex programming. 2.6. Perturbed problems. 2.7. The fundamental duality formula. 2.8. Formulas for conjugates and e-subdifferentials, duality relations and optimality conditions. 2.9. Convex optimization with constraints. 2.10. A minimax theorem. 2.11. Exercises. 2.12. Bibliographical notes -- ch. 3. Some results and applications of convex analysis in normed spaces. 3.1. Further fundamental results in convex analysis. 3.2. Convexity and monotonicity of subdifferentials. 3.3. Some classes of functions of a real variable and differentiability of convex functions. 3.4. Well conditioned functions. 3.5. Uniformly convex and uniformly smooth convex functions. 3.6. Uniformly convex and uniformly smooth convex functions on bounded sets. 3.7. Applications to the geometry of normed spaces. 3.8. Applications to the best approximation problem. 3.9. Characterizations of convexity in terms of smoothness. 3.10. Weak sharp minima, well-behaved functions and global error bounds for convex inequalities. 3.11. Monotone multifunctions. 3.12. Exercises. 3.13. Bibliographical notes. English. Convex functions. http://id.loc.gov/authorities/subjects/sh85031728 Convex sets. http://id.loc.gov/authorities/subjects/sh85031731 Functional analysis. http://id.loc.gov/authorities/subjects/sh85052312 Vector spaces. http://id.loc.gov/authorities/subjects/sh85142456 Fonctions convexes. Ensembles convexes. Analyse fonctionnelle. Espaces vectoriels. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Convex functions fast Convex sets fast Functional analysis fast Vector spaces fast has work: Convex analysis in general vector spaces (Text) https://id.oclc.org/worldcat/entity/E39PCGRWpGBh3jPDv8YRWrV9Qm https://id.oclc.org/worldcat/ontology/hasWork Print version: Zalinescu, C., 1952- Convex analysis in general vector spaces. River Edge, NJ : World Scientific, ©2002 9812380671 9789812380678 (DLC) 2002069000 (OCoLC)49959262 |
| spellingShingle | Zalinescu, C., 1952- Convex analysis in general vector spaces / Ch. 1. Preliminary results on functional analysis. 1.1. Preliminary notions and results. 1.2. Closedness and interiority notions. 1.3. Open mapping theorems. 1.4. Variational principles. 1.5. Exercises. 1.6. Bibliographical notes -- ch. 2. Convex analysis in locally convex spaces. 2.1. Convex functions. 2.2. Semi-continuity of convex functions. 2.3. Conjugate functions. 2.4. The subdifferential of a convex function. 2.5. The general problem of convex programming. 2.6. Perturbed problems. 2.7. The fundamental duality formula. 2.8. Formulas for conjugates and e-subdifferentials, duality relations and optimality conditions. 2.9. Convex optimization with constraints. 2.10. A minimax theorem. 2.11. Exercises. 2.12. Bibliographical notes -- ch. 3. Some results and applications of convex analysis in normed spaces. 3.1. Further fundamental results in convex analysis. 3.2. Convexity and monotonicity of subdifferentials. 3.3. Some classes of functions of a real variable and differentiability of convex functions. 3.4. Well conditioned functions. 3.5. Uniformly convex and uniformly smooth convex functions. 3.6. Uniformly convex and uniformly smooth convex functions on bounded sets. 3.7. Applications to the geometry of normed spaces. 3.8. Applications to the best approximation problem. 3.9. Characterizations of convexity in terms of smoothness. 3.10. Weak sharp minima, well-behaved functions and global error bounds for convex inequalities. 3.11. Monotone multifunctions. 3.12. Exercises. 3.13. Bibliographical notes. Convex functions. http://id.loc.gov/authorities/subjects/sh85031728 Convex sets. http://id.loc.gov/authorities/subjects/sh85031731 Functional analysis. http://id.loc.gov/authorities/subjects/sh85052312 Vector spaces. http://id.loc.gov/authorities/subjects/sh85142456 Fonctions convexes. Ensembles convexes. Analyse fonctionnelle. Espaces vectoriels. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Convex functions fast Convex sets fast Functional analysis fast Vector spaces fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85031728 http://id.loc.gov/authorities/subjects/sh85031731 http://id.loc.gov/authorities/subjects/sh85052312 http://id.loc.gov/authorities/subjects/sh85142456 |
| title | Convex analysis in general vector spaces / |
| title_auth | Convex analysis in general vector spaces / |
| title_exact_search | Convex analysis in general vector spaces / |
| title_full | Convex analysis in general vector spaces / C Zălinescu. |
| title_fullStr | Convex analysis in general vector spaces / C Zălinescu. |
| title_full_unstemmed | Convex analysis in general vector spaces / C Zălinescu. |
| title_short | Convex analysis in general vector spaces / |
| title_sort | convex analysis in general vector spaces |
| topic | Convex functions. http://id.loc.gov/authorities/subjects/sh85031728 Convex sets. http://id.loc.gov/authorities/subjects/sh85031731 Functional analysis. http://id.loc.gov/authorities/subjects/sh85052312 Vector spaces. http://id.loc.gov/authorities/subjects/sh85142456 Fonctions convexes. Ensembles convexes. Analyse fonctionnelle. Espaces vectoriels. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Convex functions fast Convex sets fast Functional analysis fast Vector spaces fast |
| topic_facet | Convex functions. Convex sets. Functional analysis. Vector spaces. Fonctions convexes. Ensembles convexes. Analyse fonctionnelle. Espaces vectoriels. MATHEMATICS Calculus. MATHEMATICS Mathematical Analysis. Convex functions Convex sets Functional analysis Vector spaces |
| work_keys_str_mv | AT zalinescuc convexanalysisingeneralvectorspaces |