Ontology type: schema:Book

1999

Monograph

Springer Nature

As is well known, Pontryagin's maximum principle and Bellman's dynamic programming are the two principal and most commonly used approaches in solving stochastic optimal control problems. * An interesting phenomenon one can observe from the literature is that these two approaches have been developed separately and independently. Since both methods are used to investigate the same problems, a natural question one will ask is the fol lowing: (Q) What is the relationship betwccn the maximum principlc and dy namic programming in stochastic optimal controls? There did exist some researches (prior to the 1980s) on the relationship between these two. Nevertheless, the results usually werestated in heuristic terms and proved under rather restrictive assumptions, which were not satisfied in most cases. In the statement of a Pontryagin-type maximum principle there is an adjoint equation, which is an ordinary differential equation (ODE) in the (finite-dimensional) deterministic case and a stochastic differential equation (SDE) in the stochastic case. The system consisting of the adjoint equa tion, the original state equation, and the maximum condition is referred to as an (extended) Hamiltonian system. On the other hand, in Bellman's dynamic programming, there is a partial differential equation (PDE), of first order in the (finite-dimensional) deterministic case and of second or der in the stochastic case. This is known as a Hamilton-Jacobi-Bellman (HJB) equation. More... »

http://scigraph.springernature.com/pub.10.1007/978-1-4612-1466-3

http://dx.doi.org/10.1007/978-1-4612-1466-3

978-1-4612-7154-3 | 978-1-4612-1466-3

https://app.dimensions.ai/details/publication/pub.1013764448

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/2008/0102",
"inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/",
"name": "Applied Mathematics",
"type": "DefinedTerm"
},
{
"id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0103",
"inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/",
"name": "Numerical and Computational Mathematics",
"type": "DefinedTerm"
},
{
"id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0104",
"inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/",
"name": "Statistics",
"type": "DefinedTerm"
}
],
"author": [
{
"affiliation": {
"alternateName": "Department of Mathematics, Fudan University, 200433, Shanghai, China",
"id": "http://www.grid.ac/institutes/grid.8547.e",
"name": [
"Department of Mathematics, Fudan University, 200433, Shanghai, China"
],
"type": "Organization"
},
"familyName": "Yong",
"givenName": "Jiongmin",
"id": "sg:person.07412444115.67",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07412444115.67"
],
"type": "Person"
},
{
"affiliation": {
"alternateName": "Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong",
"id": "http://www.grid.ac/institutes/grid.10784.3a",
"name": [
"Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong"
],
"type": "Organization"
},
"familyName": "Zhou",
"givenName": "Xun Yu",
"id": "sg:person.015334117131.84",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015334117131.84"
],
"type": "Person"
}
],
"datePublished": "1999",
"datePublishedReg": "1999-01-01",
"description": "As is well known, Pontryagin's maximum principle and Bellman's dynamic programming are the two principal and most commonly used approaches in solving stochastic optimal control problems. * An interesting phenomenon one can observe from the literature is that these two approaches have been developed separately and independently. Since both methods are used to investigate the same problems, a natural question one will ask is the fol\u00ad lowing: (Q) What is the relationship betwccn the maximum principlc and dy\u00ad namic programming in stochastic optimal controls? There did exist some researches (prior to the 1980s) on the relationship between these two. Nevertheless, the results usually werestated in heuristic terms and proved under rather restrictive assumptions, which were not satisfied in most cases. In the statement of a Pontryagin-type maximum principle there is an adjoint equation, which is an ordinary differential equation (ODE) in the (finite-dimensional) deterministic case and a stochastic differential equation (SDE) in the stochastic case. The system consisting of the adjoint equa\u00ad tion, the original state equation, and the maximum condition is referred to as an (extended) Hamiltonian system. On the other hand, in Bellman's dynamic programming, there is a partial differential equation (PDE), of first order in the (finite-dimensional) deterministic case and of second or\u00ad der in the stochastic case. This is known as a Hamilton-Jacobi-Bellman (HJB) equation.",
"genre": "monograph",
"id": "sg:pub.10.1007/978-1-4612-1466-3",
"inLanguage": "en",
"isAccessibleForFree": false,
"isbn": [
"978-1-4612-7154-3",
"978-1-4612-1466-3"
],
"keywords": [
"stochastic differential equations",
"partial differential equations",
"ordinary differential equations",
"Bellman's dynamic programming",
"differential equations",
"maximum principle",
"dynamic programming",
"stochastic case",
"Hamiltonian systems",
"deterministic case",
"Pontryagin-type maximum principle",
"stochastic optimal control problem",
"stochastic optimal control",
"optimal control problem",
"Hamilton-Jacobi",
"Pontryagin maximum principle",
"original state equation",
"stochastic control",
"HJB equation",
"Bellman equation",
"adjoint equations",
"optimal control",
"control problem",
"state equation",
"restrictive assumptions",
"equations",
"natural question",
"heuristic terms",
"same problem",
"programming",
"first order",
"maximum conditions",
"problem",
"adjoint",
"interesting phenomenon",
"system",
"approach",
"principles",
"assumption",
"DERs",
"control",
"cases",
"terms",
"order",
"statements",
"conditions",
"phenomenon",
"most cases",
"results",
"tion",
"literature",
"questions",
"hand",
"relationship",
"research",
"principals",
"method",
"maximum principlc",
"principlc",
"namic programming"
],
"name": "Stochastic Controls, Hamiltonian Systems and HJB Equations",
"productId": [
{
"name": "dimensions_id",
"type": "PropertyValue",
"value": [
"pub.1013764448"
]
},
{
"name": "doi",
"type": "PropertyValue",
"value": [
"10.1007/978-1-4612-1466-3"
]
}
],
"publisher": {
"name": "Springer Nature",
"type": "Organisation"
},
"sameAs": [
"https://doi.org/10.1007/978-1-4612-1466-3",
"https://app.dimensions.ai/details/publication/pub.1013764448"
],
"sdDataset": "books",
"sdDatePublished": "2022-01-01T19:05",
"sdLicense": "https://scigraph.springernature.com/explorer/license/",
"sdPublisher": {
"name": "Springer Nature - SN SciGraph project",
"type": "Organization"
},
"sdSource": "s3://com-springernature-scigraph/baseset/20220101/entities/gbq_results/book/book_25.jsonl",
"type": "Book",
"url": "https://doi.org/10.1007/978-1-4612-1466-3"
}
]
```

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

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.10.1007/978-1-4612-1466-3'

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

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-1-4612-1466-3'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-1-4612-1466-3'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-1-4612-1466-3'

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

128 TRIPLES
21 PREDICATES
87 URIs
78 LITERALS
5 BLANK NODES

Subject | Predicate | Object | |
---|---|---|---|

1 | sg:pub.10.1007/978-1-4612-1466-3 | schema:about | anzsrc-for:01 |

2 | ″ | ″ | anzsrc-for:0102 |

3 | ″ | ″ | anzsrc-for:0103 |

4 | ″ | ″ | anzsrc-for:0104 |

5 | ″ | schema:author | N887d5b7745e6409baf571801deec5a4a |

6 | ″ | schema:datePublished | 1999 |

7 | ″ | schema:datePublishedReg | 1999-01-01 |

8 | ″ | schema:description | As is well known, Pontryagin's maximum principle and Bellman's dynamic programming are the two principal and most commonly used approaches in solving stochastic optimal control problems. * An interesting phenomenon one can observe from the literature is that these two approaches have been developed separately and independently. Since both methods are used to investigate the same problems, a natural question one will ask is the fol lowing: (Q) What is the relationship betwccn the maximum principlc and dy namic programming in stochastic optimal controls? There did exist some researches (prior to the 1980s) on the relationship between these two. Nevertheless, the results usually werestated in heuristic terms and proved under rather restrictive assumptions, which were not satisfied in most cases. In the statement of a Pontryagin-type maximum principle there is an adjoint equation, which is an ordinary differential equation (ODE) in the (finite-dimensional) deterministic case and a stochastic differential equation (SDE) in the stochastic case. The system consisting of the adjoint equa tion, the original state equation, and the maximum condition is referred to as an (extended) Hamiltonian system. On the other hand, in Bellman's dynamic programming, there is a partial differential equation (PDE), of first order in the (finite-dimensional) deterministic case and of second or der in the stochastic case. This is known as a Hamilton-Jacobi-Bellman (HJB) equation. |

9 | ″ | schema:genre | monograph |

10 | ″ | schema:inLanguage | en |

11 | ″ | schema:isAccessibleForFree | false |

12 | ″ | schema:isbn | 978-1-4612-1466-3 |

13 | ″ | ″ | 978-1-4612-7154-3 |

14 | ″ | schema:keywords | Bellman equation |

15 | ″ | ″ | Bellman's dynamic programming |

16 | ″ | ″ | DERs |

17 | ″ | ″ | HJB equation |

18 | ″ | ″ | Hamilton-Jacobi |

19 | ″ | ″ | Hamiltonian systems |

20 | ″ | ″ | Pontryagin maximum principle |

21 | ″ | ″ | Pontryagin-type maximum principle |

22 | ″ | ″ | adjoint |

23 | ″ | ″ | adjoint equations |

24 | ″ | ″ | approach |

25 | ″ | ″ | assumption |

26 | ″ | ″ | cases |

27 | ″ | ″ | conditions |

28 | ″ | ″ | control |

29 | ″ | ″ | control problem |

30 | ″ | ″ | deterministic case |

31 | ″ | ″ | differential equations |

32 | ″ | ″ | dynamic programming |

33 | ″ | ″ | equations |

34 | ″ | ″ | first order |

35 | ″ | ″ | hand |

36 | ″ | ″ | heuristic terms |

37 | ″ | ″ | interesting phenomenon |

38 | ″ | ″ | literature |

39 | ″ | ″ | maximum conditions |

40 | ″ | ″ | maximum principlc |

41 | ″ | ″ | maximum principle |

42 | ″ | ″ | method |

43 | ″ | ″ | most cases |

44 | ″ | ″ | namic programming |

45 | ″ | ″ | natural question |

46 | ″ | ″ | optimal control |

47 | ″ | ″ | optimal control problem |

48 | ″ | ″ | order |

49 | ″ | ″ | ordinary differential equations |

50 | ″ | ″ | original state equation |

51 | ″ | ″ | partial differential equations |

52 | ″ | ″ | phenomenon |

53 | ″ | ″ | principals |

54 | ″ | ″ | principlc |

55 | ″ | ″ | principles |

56 | ″ | ″ | problem |

57 | ″ | ″ | programming |

58 | ″ | ″ | questions |

59 | ″ | ″ | relationship |

60 | ″ | ″ | research |

61 | ″ | ″ | restrictive assumptions |

62 | ″ | ″ | results |

63 | ″ | ″ | same problem |

64 | ″ | ″ | state equation |

65 | ″ | ″ | statements |

66 | ″ | ″ | stochastic case |

67 | ″ | ″ | stochastic control |

68 | ″ | ″ | stochastic differential equations |

69 | ″ | ″ | stochastic optimal control |

70 | ″ | ″ | stochastic optimal control problem |

71 | ″ | ″ | system |

72 | ″ | ″ | terms |

73 | ″ | ″ | tion |

74 | ″ | schema:name | Stochastic Controls, Hamiltonian Systems and HJB Equations |

75 | ″ | schema:productId | N5b70ca1d38da475183ce05f1bce8bffd |

76 | ″ | ″ | N5baf30e6d9f54e01820829f200bc9884 |

77 | ″ | schema:publisher | Ncdfb3247fa624e8fa4432ea67f247ec5 |

78 | ″ | schema:sameAs | https://app.dimensions.ai/details/publication/pub.1013764448 |

79 | ″ | ″ | https://doi.org/10.1007/978-1-4612-1466-3 |

80 | ″ | schema:sdDatePublished | 2022-01-01T19:05 |

81 | ″ | schema:sdLicense | https://scigraph.springernature.com/explorer/license/ |

82 | ″ | schema:sdPublisher | N7c218b33120f4337b17edb255c112628 |

83 | ″ | schema:url | https://doi.org/10.1007/978-1-4612-1466-3 |

84 | ″ | sgo:license | sg:explorer/license/ |

85 | ″ | sgo:sdDataset | books |

86 | ″ | rdf:type | schema:Book |

87 | N2e0a8c47735f4b758983744b40b9f834 | rdf:first | sg:person.015334117131.84 |

88 | ″ | rdf:rest | rdf:nil |

89 | N5b70ca1d38da475183ce05f1bce8bffd | schema:name | dimensions_id |

90 | ″ | schema:value | pub.1013764448 |

91 | ″ | rdf:type | schema:PropertyValue |

92 | N5baf30e6d9f54e01820829f200bc9884 | schema:name | doi |

93 | ″ | schema:value | 10.1007/978-1-4612-1466-3 |

94 | ″ | rdf:type | schema:PropertyValue |

95 | N7c218b33120f4337b17edb255c112628 | schema:name | Springer Nature - SN SciGraph project |

96 | ″ | rdf:type | schema:Organization |

97 | N887d5b7745e6409baf571801deec5a4a | rdf:first | sg:person.07412444115.67 |

98 | ″ | rdf:rest | N2e0a8c47735f4b758983744b40b9f834 |

99 | Ncdfb3247fa624e8fa4432ea67f247ec5 | schema:name | Springer Nature |

100 | ″ | rdf:type | schema:Organisation |

101 | anzsrc-for:01 | schema:inDefinedTermSet | anzsrc-for: |

102 | ″ | schema:name | Mathematical Sciences |

103 | ″ | rdf:type | schema:DefinedTerm |

104 | anzsrc-for:0102 | schema:inDefinedTermSet | anzsrc-for: |

105 | ″ | schema:name | Applied Mathematics |

106 | ″ | rdf:type | schema:DefinedTerm |

107 | anzsrc-for:0103 | schema:inDefinedTermSet | anzsrc-for: |

108 | ″ | schema:name | Numerical and Computational Mathematics |

109 | ″ | rdf:type | schema:DefinedTerm |

110 | anzsrc-for:0104 | schema:inDefinedTermSet | anzsrc-for: |

111 | ″ | schema:name | Statistics |

112 | ″ | rdf:type | schema:DefinedTerm |

113 | sg:person.015334117131.84 | schema:affiliation | grid-institutes:grid.10784.3a |

114 | ″ | schema:familyName | Zhou |

115 | ″ | schema:givenName | Xun Yu |

116 | ″ | schema:sameAs | https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015334117131.84 |

117 | ″ | rdf:type | schema:Person |

118 | sg:person.07412444115.67 | schema:affiliation | grid-institutes:grid.8547.e |

119 | ″ | schema:familyName | Yong |

120 | ″ | schema:givenName | Jiongmin |

121 | ″ | schema:sameAs | https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07412444115.67 |

122 | ″ | rdf:type | schema:Person |

123 | grid-institutes:grid.10784.3a | schema:alternateName | Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong |

124 | ″ | schema:name | Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong |

125 | ″ | rdf:type | schema:Organization |

126 | grid-institutes:grid.8547.e | schema:alternateName | Department of Mathematics, Fudan University, 200433, Shanghai, China |

127 | ″ | schema:name | Department of Mathematics, Fudan University, 200433, Shanghai, China |

128 | ″ | rdf:type | schema:Organization |