An invitation to optimal transport, Wasserstein distances, and gradient flows:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
EMS Press
[2023]
|
| Ausgabe: | 2. edition |
| Schriftenreihe: | EMS textbooks in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | vi, 146 Seiten 24 cm |
| ISBN: | 9783985470501 3985470502 |
Internformat
MARC
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| 100 | 1 | |a Figalli, Alessio |d 1984- |e Verfasser |0 (DE-588)1122674147 |4 aut | |
| 245 | 1 | 0 | |a An invitation to optimal transport, Wasserstein distances, and gradient flows |c Alessio Figalli, Federico Glaudo |
| 250 | |a 2. edition | ||
| 264 | 1 | |a Berlin |b EMS Press |c [2023] | |
| 300 | |a vi, 146 Seiten |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a EMS textbooks in mathematics | |
| 650 | 0 | 7 | |a Gradientenfluss |0 (DE-588)4841287-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Optimale Kontrolle |0 (DE-588)4121428-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Transportproblem |0 (DE-588)4060694-6 |2 gnd |9 rswk-swf |
| 653 | |a optimal transport | ||
| 653 | |a Wasserstein distance | ||
| 653 | |a duality | ||
| 653 | |a gradient flows | ||
| 653 | |a measure theory | ||
| 653 | |a displacement convexity | ||
| 689 | 0 | 0 | |a Optimale Kontrolle |0 (DE-588)4121428-6 |D s |
| 689 | 0 | 1 | |a Transportproblem |0 (DE-588)4060694-6 |D s |
| 689 | 0 | 2 | |a Gradientenfluss |0 (DE-588)4841287-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Glaudo, Federico |d 1994- |e Verfasser |0 (DE-588)1236384768 |4 aut | |
| 710 | 2 | |a European Mathematical Society Publishing House ETH-Zentrum SEW A27 |0 (DE-588)1066118477 |4 pbl | |
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Datensatz im Suchindex
| _version_ | 1804185916661563392 |
|---|---|
| adam_text | CONTENTS
1
INTRODUCTION
.......................................................................................................
1
1.1
HISTORICAL
OVERVIEW
....................................................................................
1
1.2
PUSH-FORWARD
OF
MEASURES
........................................................................
2
1.3
BASICS
OF
RIEMANNIAN
GEOMETRY
..............................................................
5
1.4
TRANSPORT
MAPS
........................................................................................
7
1.5
AN
APPLICATION
TO
ISOPERIMETRIC
INEQUALITIES
..........................................
14
1.6
A
JACOBIAN
EQUATION
FOR
TRANSPORT
MAPS
..................................................
16
2
OPTIMAL
TRANSPORT
...........................................................................................
17
2.1
PRELIMINARIES
IN
MEASURE
THEORY
..............................................................
17
2.2
MONGE
VS.
KANTOROVICH
............................................................................
24
2.3
EXISTENCE
OF
AN
OPTIMAL
COUPLING
...........................................................
24
2.4
C
-CYCLICAL
MONOTONICITY
............................................................................
26
2.5
THE
CASE
C(X,
Y)
=
XZY2
ON
X
=
Y
=
RD
..........................................
29
2.6
GENERAL
COST
FUNCTIONS:
KANTOROVICH
DUALITY
...........................................
49
2.7
GENERAL
COST
FUNCTIONS:
EXISTENCE
AND
UNIQUENESS
OF
OPTIMAL
TRANSPORT
MAPS
..........................................................................................
55
3
WASSERSTEIN
DISTANCES
AND
GRADIENT
FLOWS
...................................................
59
3.1
P-WASSERSTEIN
DISTANCES
AND
GEODESICS
.................................................
59
3.2
AN
INFORMAL
INTRODUCTION
TO
GRADIENT
FLOWS
IN
HILBERT
SPACES
...............
66
3.3
HEAT
EQUATION
AND
OPTIMAL
TRANSPORT:
THE
JKO
SCHEME
........................
71
4
DIFFERENTIAL
VIEWPOINT
OF
OPTIMAL
TRANSPORT
.................................................
83
4.1
THE
CONTINUITY
EQUATION
AND
BENAMOU-BRENIER
FORMULA
.......................
83
4.2
OTTO
S
CALCULUS:
FROM
BENAMOU-BRENIER
TO
A
RIEMANNIAN
STRUCTURE
.
.
86
4.3
DISPLACEMENT
CONVEXITY
.........................................................................
91
4.4
AN
EXCURSION
INTO
THE
LINEAR
FOKKER-PLANCK
EQUATION
...........................
94
5
FURTHER
READING
.................................................................................................
103
5.1
FUNCTIONAL
AND
GEOMETRIC
INEQUALITIES
......................................................
104
5.2
PROBABILITY
..................................................................................................
106
5.3
MULTI-MARGINAL
OPTIMAL
TRANSPORT
.............................................................
109
5.4
GRADIENT
FLOWS
.............................................................................................
ILL
5.5
REGULARITY
THEORY
........................................................................................
112
5.6
COMPUTATIONAL
ASPECTS
..............................................................................
114
5.7
FROM
RD
TO
RIEMANNIAN
MANIFOLDS
AND
BEYOND:
CD
SPACES
...............
116
VI
CONTENTS
A
EXERCISES
ON
OPTIMAL
TRANSPORT
(WITH
SOLUTIONS)
............................................
119
B
DISINTEGRATING
THE
DISINTEGRATION
THEOREM
......................................................
141
REFERENCES
...................................................................................................................
143
|
| adam_txt |
CONTENTS
1
INTRODUCTION
.
1
1.1
HISTORICAL
OVERVIEW
.
1
1.2
PUSH-FORWARD
OF
MEASURES
.
2
1.3
BASICS
OF
RIEMANNIAN
GEOMETRY
.
5
1.4
TRANSPORT
MAPS
.
7
1.5
AN
APPLICATION
TO
ISOPERIMETRIC
INEQUALITIES
.
14
1.6
A
JACOBIAN
EQUATION
FOR
TRANSPORT
MAPS
.
16
2
OPTIMAL
TRANSPORT
.
17
2.1
PRELIMINARIES
IN
MEASURE
THEORY
.
17
2.2
MONGE
VS.
KANTOROVICH
.
24
2.3
EXISTENCE
OF
AN
OPTIMAL
COUPLING
.
24
2.4
C
-CYCLICAL
MONOTONICITY
.
26
2.5
THE
CASE
C(X,
Y)
=
XZY2
ON
X
=
Y
=
RD
.
29
2.6
GENERAL
COST
FUNCTIONS:
KANTOROVICH
DUALITY
.
49
2.7
GENERAL
COST
FUNCTIONS:
EXISTENCE
AND
UNIQUENESS
OF
OPTIMAL
TRANSPORT
MAPS
.
55
3
WASSERSTEIN
DISTANCES
AND
GRADIENT
FLOWS
.
59
3.1
P-WASSERSTEIN
DISTANCES
AND
GEODESICS
.
59
3.2
AN
INFORMAL
INTRODUCTION
TO
GRADIENT
FLOWS
IN
HILBERT
SPACES
.
66
3.3
HEAT
EQUATION
AND
OPTIMAL
TRANSPORT:
THE
JKO
SCHEME
.
71
4
DIFFERENTIAL
VIEWPOINT
OF
OPTIMAL
TRANSPORT
.
83
4.1
THE
CONTINUITY
EQUATION
AND
BENAMOU-BRENIER
FORMULA
.
83
4.2
OTTO
'
S
CALCULUS:
FROM
BENAMOU-BRENIER
TO
A
RIEMANNIAN
STRUCTURE
.
.
86
4.3
DISPLACEMENT
CONVEXITY
.
91
4.4
AN
EXCURSION
INTO
THE
LINEAR
FOKKER-PLANCK
EQUATION
.
94
5
FURTHER
READING
.
103
5.1
FUNCTIONAL
AND
GEOMETRIC
INEQUALITIES
.
104
5.2
PROBABILITY
.
106
5.3
MULTI-MARGINAL
OPTIMAL
TRANSPORT
.
109
5.4
GRADIENT
FLOWS
.
ILL
5.5
REGULARITY
THEORY
.
112
5.6
COMPUTATIONAL
ASPECTS
.
114
5.7
FROM
RD
TO
RIEMANNIAN
MANIFOLDS
AND
BEYOND:
CD
SPACES
.
116
VI
CONTENTS
A
EXERCISES
ON
OPTIMAL
TRANSPORT
(WITH
SOLUTIONS)
.
119
B
DISINTEGRATING
THE
DISINTEGRATION
THEOREM
.
141
REFERENCES
.
143 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Figalli, Alessio 1984- Glaudo, Federico 1994- |
| author_GND | (DE-588)1122674147 (DE-588)1236384768 |
| author_facet | Figalli, Alessio 1984- Glaudo, Federico 1994- |
| author_role | aut aut |
| author_sort | Figalli, Alessio 1984- |
| author_variant | a f af f g fg |
| building | Verbundindex |
| bvnumber | BV049370494 |
| ctrlnum | (OCoLC)1379243038 (DE-599)DNB1289269564 |
| dewey-full | 519.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.6 |
| dewey-search | 519.6 |
| dewey-sort | 3519.6 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 2. edition |
| format | Book |
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| id | DE-604.BV049370494 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T22:54:21Z |
| indexdate | 2024-07-10T10:02:50Z |
| institution | BVB |
| institution_GND | (DE-588)1066118477 |
| isbn | 9783985470501 3985470502 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-034630454 |
| oclc_num | 1379243038 |
| open_access_boolean | |
| owner | DE-634 |
| owner_facet | DE-634 |
| physical | vi, 146 Seiten 24 cm |
| publishDate | 2023 |
| publishDateSearch | 2023 |
| publishDateSort | 2023 |
| publisher | EMS Press |
| record_format | marc |
| series2 | EMS textbooks in mathematics |
| spelling | Figalli, Alessio 1984- Verfasser (DE-588)1122674147 aut An invitation to optimal transport, Wasserstein distances, and gradient flows Alessio Figalli, Federico Glaudo 2. edition Berlin EMS Press [2023] vi, 146 Seiten 24 cm txt rdacontent n rdamedia nc rdacarrier EMS textbooks in mathematics Gradientenfluss (DE-588)4841287-9 gnd rswk-swf Optimale Kontrolle (DE-588)4121428-6 gnd rswk-swf Transportproblem (DE-588)4060694-6 gnd rswk-swf optimal transport Wasserstein distance duality gradient flows measure theory displacement convexity Optimale Kontrolle (DE-588)4121428-6 s Transportproblem (DE-588)4060694-6 s Gradientenfluss (DE-588)4841287-9 s DE-604 Glaudo, Federico 1994- Verfasser (DE-588)1236384768 aut European Mathematical Society Publishing House ETH-Zentrum SEW A27 (DE-588)1066118477 pbl Erscheint auch als Online-Ausgabe 978-3-98547-550-6 Vorangegangen ist 9783985470105 B:DE-101 application/pdf https://d-nb.info/1289269564/04 Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034630454&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p dnb 20230921 DE-101 https://d-nb.info/provenance/plan#dnb |
| spellingShingle | Figalli, Alessio 1984- Glaudo, Federico 1994- An invitation to optimal transport, Wasserstein distances, and gradient flows Gradientenfluss (DE-588)4841287-9 gnd Optimale Kontrolle (DE-588)4121428-6 gnd Transportproblem (DE-588)4060694-6 gnd |
| subject_GND | (DE-588)4841287-9 (DE-588)4121428-6 (DE-588)4060694-6 |
| title | An invitation to optimal transport, Wasserstein distances, and gradient flows |
| title_auth | An invitation to optimal transport, Wasserstein distances, and gradient flows |
| title_exact_search | An invitation to optimal transport, Wasserstein distances, and gradient flows |
| title_exact_search_txtP | An invitation to optimal transport, Wasserstein distances, and gradient flows |
| title_full | An invitation to optimal transport, Wasserstein distances, and gradient flows Alessio Figalli, Federico Glaudo |
| title_fullStr | An invitation to optimal transport, Wasserstein distances, and gradient flows Alessio Figalli, Federico Glaudo |
| title_full_unstemmed | An invitation to optimal transport, Wasserstein distances, and gradient flows Alessio Figalli, Federico Glaudo |
| title_short | An invitation to optimal transport, Wasserstein distances, and gradient flows |
| title_sort | an invitation to optimal transport wasserstein distances and gradient flows |
| topic | Gradientenfluss (DE-588)4841287-9 gnd Optimale Kontrolle (DE-588)4121428-6 gnd Transportproblem (DE-588)4060694-6 gnd |
| topic_facet | Gradientenfluss Optimale Kontrolle Transportproblem |
| url | https://d-nb.info/1289269564/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034630454&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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