Convex Analysis and Monotone Operator Theory in Hilbert Spaces View Full Text


Ontology type: schema:Book     


Book Info

DATE

2011

GENRE

Monograph

AUTHORS

Heinz H. Bauschke , Patrick L. Combettes

PUBLISHER

Springer Nature

ABSTRACT

This book presents a largely self-contained account of the main results of convex analysis, monotone operator theory, and the theory of nonexpansive operators in the context of Hilbert spaces. Unlike existing literature, the novelty of this book, and indeed its central theme, is the tight interplay among the key notions of convexity, monotonicity, and nonexpansiveness. The presentation is accessible to a broad audience and attempts to reach out in particular to the applied sciences and engineering communities, where these tools have become indispensable. Graduate students and researchers in pure and applied mathematics will benefit from this book. It is also directed to researchers in engineering, decision sciences, economics, and inverse problems, and can serve as a reference book. Author Information: Heinz H. Bauschke is a Professor of Mathematics at the University of British Columbia, Okanagan campus (UBCO) and currently a Canada Research Chair in Convex Analysis and Optimization. He was born in Frankfurt where he received his "Diplom-Mathematiker (mit Auszeichnung)" from Goethe Universität in 1990. He defended his Ph.D. thesis in Mathematics at Simon Fraser University in 1996 and was awarded the Governor General's Gold Medal for his graduate work. After a NSERC Postdoctoral Fellowship spent at the University of Waterloo, at the Pennsylvania State University, and at the University of California at Santa Barbara, Dr. Bauschke became College Professor at Okanagan University College in 1998. He joined the University of Guelph in 2001, and he returned to Kelowna in 2005, when Okanagan University College turned into UBCO. In 2009, he became UBCO's first "Researcher of the Year". Patrick L. Combettes received the Brevet d'Études du Premier Cycle from Académie de Versailles in 1977 and the Ph.D. degree from North Carolina State University in 1989. In 1990, he joined the City College and the Graduate Center of the City University of New York where he became a Full Professor in 1999. Since 1999, he has been with the Faculty of Mathematics of Université Pierre et Marie Curie -- Paris 6, laboratoire Jacques-Louis Lions, where he is presently a Professeur de Classe Exceptionnelle. He was elected Fellow of the IEEE in 2005. More... »

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-1-4419-9467-7

DOI

http://dx.doi.org/10.1007/978-1-4419-9467-7

ISBN

978-1-4419-9466-0 | 978-1-4419-9467-7

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1044558790


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Pure Mathematics", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Okanagan Campus, Department of  Mathematics and Statistic, University of British Columbia, V1V 1V7, Kelowna, British Columbia, Canada", 
          "id": "http://www.grid.ac/institutes/grid.17091.3e", 
          "name": [
            "Okanagan Campus, Department of  Mathematics and Statistic, University of British Columbia, V1V 1V7, Kelowna, British Columbia, Canada"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Bauschke", 
        "givenName": "Heinz H.", 
        "id": "sg:person.011533473347.47", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011533473347.47"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Laboratoire Jacques-Louis Lions, Universit\u00e9 Pierre et Marie Curie, Place Jussieu 4, 75005, Paris, France", 
          "id": "http://www.grid.ac/institutes/grid.464004.2", 
          "name": [
            "Laboratoire Jacques-Louis Lions, Universit\u00e9 Pierre et Marie Curie, Place Jussieu 4, 75005, Paris, France"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Combettes", 
        "givenName": "Patrick L.", 
        "id": "sg:person.011005613201.45", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011005613201.45"
        ], 
        "type": "Person"
      }
    ], 
    "datePublished": "2011", 
    "datePublishedReg": "2011-01-01", 
    "description": "This book presents a largely self-contained account of the main results of convex analysis, monotone operator theory, and the theory of nonexpansive operators in the context of Hilbert spaces. Unlike existing literature, the novelty of this book, and indeed its central theme, is the tight interplay among the key notions of convexity, monotonicity, and nonexpansiveness. The presentation is accessible to a broad audience and attempts to reach out in particular to the applied sciences and engineering communities, where these tools have become indispensable. Graduate students and researchers in pure and applied mathematics will benefit from this book. It is also directed to researchers in engineering, decision sciences, economics, and inverse problems, and can serve as a reference book. Author Information: Heinz H. Bauschke is a Professor of Mathematics at the University of British Columbia, Okanagan campus (UBCO) and currently a Canada Research Chair in Convex Analysis and Optimization. He was born in Frankfurt where he received his \"Diplom-Mathematiker (mit Auszeichnung)\" from Goethe Universit\u00e4t in 1990. He defended his Ph.D. thesis in Mathematics at Simon Fraser University in 1996 and was awarded the Governor General's Gold Medal for his graduate work. After a NSERC Postdoctoral Fellowship spent at the University of Waterloo, at the Pennsylvania State University, and at the University of California at Santa Barbara, Dr. Bauschke became College Professor at Okanagan University College in 1998. He joined the University of Guelph in 2001, and he returned to Kelowna in 2005, when Okanagan University College turned into UBCO. In 2009, he became UBCO's first \"Researcher of the Year\". Patrick L. Combettes received the Brevet d'\u00c9tudes du Premier Cycle from Acad\u00e9mie de Versailles in 1977 and the Ph.D. degree from North Carolina State University in 1989. In 1990, he joined the City College and the Graduate Center of the City University of New York where he became a Full Professor in 1999. Since 1999, he has been with the Faculty of Mathematics of Universit\u00e9 Pierre et Marie Curie -- Paris 6, laboratoire Jacques-Louis Lions, where he is presently a Professeur de Classe Exceptionnelle. He was elected Fellow of the IEEE in 2005.", 
    "genre": "monograph", 
    "id": "sg:pub.10.1007/978-1-4419-9467-7", 
    "isAccessibleForFree": false, 
    "isbn": [
      "978-1-4419-9466-0", 
      "978-1-4419-9467-7"
    ], 
    "keywords": [
      "monotone operator theory", 
      "convex analysis", 
      "operator theory", 
      "Hilbert space", 
      "self-contained account", 
      "Jacques-Louis Lions", 
      "Professor of Mathematics", 
      "applied mathematics", 
      "nonexpansive operators", 
      "inverse problem", 
      "Bauschke", 
      "mathematics", 
      "Faculty of Mathematics", 
      "Universit\u00e9 Pierre", 
      "theory", 
      "main results", 
      "Ph.D. thesis", 
      "nonexpansiveness", 
      "space", 
      "Combettes", 
      "key notions", 
      "monotonicity", 
      "University of Waterloo", 
      "operators", 
      "engineering community", 
      "convexity", 
      "decision science", 
      "optimization", 
      "IEEE", 
      "Ph.D. degree", 
      "Curie", 
      "problem", 
      "graduate students", 
      "reference books", 
      "gold medal", 
      "Pennsylvania State University", 
      "City College", 
      "account", 
      "broad audience", 
      "novelty", 
      "science", 
      "State University", 
      "analysis", 
      "notion", 
      "North Carolina State University", 
      "interplay", 
      "engineering", 
      "tool", 
      "researchers", 
      "work", 
      "results", 
      "Marie Curie", 
      "book", 
      "postdoctoral fellowship", 
      "graduate work", 
      "central theme", 
      "lions", 
      "degree", 
      "Medal", 
      "University of California", 
      "literature", 
      "Santa Barbara", 
      "full professors", 
      "Waterloo", 
      "economics", 
      "Universit\u00e4t", 
      "center", 
      "City University", 
      "tight interplay", 
      "context", 
      "Pierre", 
      "professors", 
      "attempt", 
      "University", 
      "Simon Fraser University", 
      "Barbara", 
      "thesis", 
      "Research Chair", 
      "cycle", 
      "presentation", 
      "students", 
      "Kelowna", 
      "Canada Research Chair", 
      "fellowship", 
      "fellows", 
      "Frankfurt", 
      "chair", 
      "years", 
      "Acad\u00e9mie", 
      "California", 
      "community", 
      "University College", 
      "audience", 
      "British Columbia", 
      "New York", 
      "campus", 
      "themes", 
      "Graduate Center", 
      "York", 
      "Columbia", 
      "College", 
      "faculty", 
      "Versailles", 
      "Guelph", 
      "University of Guelph", 
      "college professors"
    ], 
    "name": "Convex Analysis and Monotone Operator Theory in Hilbert Spaces", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1044558790"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/978-1-4419-9467-7"
        ]
      }
    ], 
    "publisher": {
      "name": "Springer Nature", 
      "type": "Organisation"
    }, 
    "sameAs": [
      "https://doi.org/10.1007/978-1-4419-9467-7", 
      "https://app.dimensions.ai/details/publication/pub.1044558790"
    ], 
    "sdDataset": "books", 
    "sdDatePublished": "2022-09-02T16:09", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20220902/entities/gbq_results/book/book_1.jsonl", 
    "type": "Book", 
    "url": "https://doi.org/10.1007/978-1-4419-9467-7"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/978-1-4419-9467-7'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-1-4419-9467-7'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-1-4419-9467-7'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-1-4419-9467-7'


 

This table displays all metadata directly associated to this object as RDF triples.

165 TRIPLES      20 PREDICATES      130 URIs      123 LITERALS      5 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/978-1-4419-9467-7 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author N4cc7ecbbc2804662a90a82d764370bdc
4 schema:datePublished 2011
5 schema:datePublishedReg 2011-01-01
6 schema:description This book presents a largely self-contained account of the main results of convex analysis, monotone operator theory, and the theory of nonexpansive operators in the context of Hilbert spaces. Unlike existing literature, the novelty of this book, and indeed its central theme, is the tight interplay among the key notions of convexity, monotonicity, and nonexpansiveness. The presentation is accessible to a broad audience and attempts to reach out in particular to the applied sciences and engineering communities, where these tools have become indispensable. Graduate students and researchers in pure and applied mathematics will benefit from this book. It is also directed to researchers in engineering, decision sciences, economics, and inverse problems, and can serve as a reference book. Author Information: Heinz H. Bauschke is a Professor of Mathematics at the University of British Columbia, Okanagan campus (UBCO) and currently a Canada Research Chair in Convex Analysis and Optimization. He was born in Frankfurt where he received his "Diplom-Mathematiker (mit Auszeichnung)" from Goethe Universität in 1990. He defended his Ph.D. thesis in Mathematics at Simon Fraser University in 1996 and was awarded the Governor General's Gold Medal for his graduate work. After a NSERC Postdoctoral Fellowship spent at the University of Waterloo, at the Pennsylvania State University, and at the University of California at Santa Barbara, Dr. Bauschke became College Professor at Okanagan University College in 1998. He joined the University of Guelph in 2001, and he returned to Kelowna in 2005, when Okanagan University College turned into UBCO. In 2009, he became UBCO's first "Researcher of the Year". Patrick L. Combettes received the Brevet d'Études du Premier Cycle from Académie de Versailles in 1977 and the Ph.D. degree from North Carolina State University in 1989. In 1990, he joined the City College and the Graduate Center of the City University of New York where he became a Full Professor in 1999. Since 1999, he has been with the Faculty of Mathematics of Université Pierre et Marie Curie -- Paris 6, laboratoire Jacques-Louis Lions, where he is presently a Professeur de Classe Exceptionnelle. He was elected Fellow of the IEEE in 2005.
7 schema:genre monograph
8 schema:isAccessibleForFree false
9 schema:isbn 978-1-4419-9466-0
10 978-1-4419-9467-7
11 schema:keywords Académie
12 Barbara
13 Bauschke
14 British Columbia
15 California
16 Canada Research Chair
17 City College
18 City University
19 College
20 Columbia
21 Combettes
22 Curie
23 Faculty of Mathematics
24 Frankfurt
25 Graduate Center
26 Guelph
27 Hilbert space
28 IEEE
29 Jacques-Louis Lions
30 Kelowna
31 Marie Curie
32 Medal
33 New York
34 North Carolina State University
35 Pennsylvania State University
36 Ph.D. degree
37 Ph.D. thesis
38 Pierre
39 Professor of Mathematics
40 Research Chair
41 Santa Barbara
42 Simon Fraser University
43 State University
44 University
45 University College
46 University of California
47 University of Guelph
48 University of Waterloo
49 Universität
50 Université Pierre
51 Versailles
52 Waterloo
53 York
54 account
55 analysis
56 applied mathematics
57 attempt
58 audience
59 book
60 broad audience
61 campus
62 center
63 central theme
64 chair
65 college professors
66 community
67 context
68 convex analysis
69 convexity
70 cycle
71 decision science
72 degree
73 economics
74 engineering
75 engineering community
76 faculty
77 fellows
78 fellowship
79 full professors
80 gold medal
81 graduate students
82 graduate work
83 interplay
84 inverse problem
85 key notions
86 lions
87 literature
88 main results
89 mathematics
90 monotone operator theory
91 monotonicity
92 nonexpansive operators
93 nonexpansiveness
94 notion
95 novelty
96 operator theory
97 operators
98 optimization
99 postdoctoral fellowship
100 presentation
101 problem
102 professors
103 reference books
104 researchers
105 results
106 science
107 self-contained account
108 space
109 students
110 themes
111 theory
112 thesis
113 tight interplay
114 tool
115 work
116 years
117 schema:name Convex Analysis and Monotone Operator Theory in Hilbert Spaces
118 schema:productId N13a127deb4bb468ab6e7fdae10e17ff9
119 N4aab7884854849999dcc5b0f45ad84b4
120 schema:publisher Nc470ee73c22f4569901b560785f6f3c7
121 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044558790
122 https://doi.org/10.1007/978-1-4419-9467-7
123 schema:sdDatePublished 2022-09-02T16:09
124 schema:sdLicense https://scigraph.springernature.com/explorer/license/
125 schema:sdPublisher Nda8ae39c1ab642ad98f580ec9c0067f4
126 schema:url https://doi.org/10.1007/978-1-4419-9467-7
127 sgo:license sg:explorer/license/
128 sgo:sdDataset books
129 rdf:type schema:Book
130 N13a127deb4bb468ab6e7fdae10e17ff9 schema:name dimensions_id
131 schema:value pub.1044558790
132 rdf:type schema:PropertyValue
133 N4aab7884854849999dcc5b0f45ad84b4 schema:name doi
134 schema:value 10.1007/978-1-4419-9467-7
135 rdf:type schema:PropertyValue
136 N4cc7ecbbc2804662a90a82d764370bdc rdf:first sg:person.011533473347.47
137 rdf:rest Ndb3a3de6bcbb4659898589466d437c88
138 Nc470ee73c22f4569901b560785f6f3c7 schema:name Springer Nature
139 rdf:type schema:Organisation
140 Nda8ae39c1ab642ad98f580ec9c0067f4 schema:name Springer Nature - SN SciGraph project
141 rdf:type schema:Organization
142 Ndb3a3de6bcbb4659898589466d437c88 rdf:first sg:person.011005613201.45
143 rdf:rest rdf:nil
144 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
145 schema:name Mathematical Sciences
146 rdf:type schema:DefinedTerm
147 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
148 schema:name Pure Mathematics
149 rdf:type schema:DefinedTerm
150 sg:person.011005613201.45 schema:affiliation grid-institutes:grid.464004.2
151 schema:familyName Combettes
152 schema:givenName Patrick L.
153 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011005613201.45
154 rdf:type schema:Person
155 sg:person.011533473347.47 schema:affiliation grid-institutes:grid.17091.3e
156 schema:familyName Bauschke
157 schema:givenName Heinz H.
158 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011533473347.47
159 rdf:type schema:Person
160 grid-institutes:grid.17091.3e schema:alternateName Okanagan Campus, Department of Mathematics and Statistic, University of British Columbia, V1V 1V7, Kelowna, British Columbia, Canada
161 schema:name Okanagan Campus, Department of Mathematics and Statistic, University of British Columbia, V1V 1V7, Kelowna, British Columbia, Canada
162 rdf:type schema:Organization
163 grid-institutes:grid.464004.2 schema:alternateName Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Place Jussieu 4, 75005, Paris, France
164 schema:name Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Place Jussieu 4, 75005, Paris, France
165 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...