CGS algorithms for unconstrained minimization of functions View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1975-07

AUTHORS

R. F. Dennemeyer, E. H. Mookini

ABSTRACT

In 1952, Hestenes and Stiefel first established, along with the conjugate-gradient algorithm, fundamental relations which exist between conjugate direction methods for function minimization on the one hand and Gram-Schmidt processes relative to a given positive-definite, symmetric matrix on the other. This paper is based on a recent reformulation of these relations by Hestenes which yield the conjugate Gram-Schmidt (CGS) algorithm. CGS includes a variety of function minimization routines, one of which is the conjugate-gradient routine. This paper gives the basic equations of CGS, including the form applicable to minimizing general nonquadratic functions ofn variables. Results of numerical experiments of one form of CGS on five standard test functions are presented. These results show that this version of CGS is very effective. More... »

PAGES

67-85

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf00935624

DOI

http://dx.doi.org/10.1007/bf00935624

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1014713541


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/2008/1109", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Neurosciences", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/11", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Medical and Health Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "name": [
            "Department of Mathematics, California State College, San Bernardino, California"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Dennemeyer", 
        "givenName": "R. F.", 
        "id": "sg:person.013111541222.37", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013111541222.37"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "University of Hawaii at Manoa", 
          "id": "https://www.grid.ac/institutes/grid.410445.0", 
          "name": [
            "Department of Mathematics, University of Hawaii, Honolulu, Hawaii"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Mookini", 
        "givenName": "E. H.", 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "https://doi.org/10.1093/comjnl/9.1.67", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1005173175"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1093/comjnl/6.2.163", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1018099115"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.6028/jres.049.044", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1073597164"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "1975-07", 
    "datePublishedReg": "1975-07-01", 
    "description": "In 1952, Hestenes and Stiefel first established, along with the conjugate-gradient algorithm, fundamental relations which exist between conjugate direction methods for function minimization on the one hand and Gram-Schmidt processes relative to a given positive-definite, symmetric matrix on the other. This paper is based on a recent reformulation of these relations by Hestenes which yield the conjugate Gram-Schmidt (CGS) algorithm. CGS includes a variety of function minimization routines, one of which is the conjugate-gradient routine. This paper gives the basic equations of CGS, including the form applicable to minimizing general nonquadratic functions ofn variables. Results of numerical experiments of one form of CGS on five standard test functions are presented. These results show that this version of CGS is very effective.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/bf00935624", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1044187", 
        "issn": [
          "0022-3239", 
          "1573-2878"
        ], 
        "name": "Journal of Optimization Theory and Applications", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "1-2", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "16"
      }
    ], 
    "name": "CGS algorithms for unconstrained minimization of functions", 
    "pagination": "67-85", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "4619247bc5f7f4d9919679983b75bab795a27d09ee529f6f504dee6a69f16297"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/bf00935624"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1014713541"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/bf00935624", 
      "https://app.dimensions.ai/details/publication/pub.1014713541"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-11T13:33", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000370_0000000370/records_46769_00000000.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "http://link.springer.com/10.1007/BF00935624"
  }
]
 

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/bf00935624'

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/bf00935624'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/bf00935624'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/bf00935624'


 

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

78 TRIPLES      21 PREDICATES      30 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/bf00935624 schema:about anzsrc-for:11
2 anzsrc-for:1109
3 schema:author N47c9e70673284d48ac707ef7185f0cee
4 schema:citation https://doi.org/10.1093/comjnl/6.2.163
5 https://doi.org/10.1093/comjnl/9.1.67
6 https://doi.org/10.6028/jres.049.044
7 schema:datePublished 1975-07
8 schema:datePublishedReg 1975-07-01
9 schema:description In 1952, Hestenes and Stiefel first established, along with the conjugate-gradient algorithm, fundamental relations which exist between conjugate direction methods for function minimization on the one hand and Gram-Schmidt processes relative to a given positive-definite, symmetric matrix on the other. This paper is based on a recent reformulation of these relations by Hestenes which yield the conjugate Gram-Schmidt (CGS) algorithm. CGS includes a variety of function minimization routines, one of which is the conjugate-gradient routine. This paper gives the basic equations of CGS, including the form applicable to minimizing general nonquadratic functions ofn variables. Results of numerical experiments of one form of CGS on five standard test functions are presented. These results show that this version of CGS is very effective.
10 schema:genre research_article
11 schema:inLanguage en
12 schema:isAccessibleForFree false
13 schema:isPartOf N8ef40ea37c5b4c7b818f207a9b3ef714
14 Ncc9aeadafa29498e8923bb9e19040f39
15 sg:journal.1044187
16 schema:name CGS algorithms for unconstrained minimization of functions
17 schema:pagination 67-85
18 schema:productId N44ca2f585c414a1f806986de6731fae6
19 Nb6bcbcab55f64d86971e9cc3655af56c
20 Ndee3f030d71c499d991e3a1918363cc5
21 schema:sameAs https://app.dimensions.ai/details/publication/pub.1014713541
22 https://doi.org/10.1007/bf00935624
23 schema:sdDatePublished 2019-04-11T13:33
24 schema:sdLicense https://scigraph.springernature.com/explorer/license/
25 schema:sdPublisher Nd93ea7a53b064570b94180f6f6345db3
26 schema:url http://link.springer.com/10.1007/BF00935624
27 sgo:license sg:explorer/license/
28 sgo:sdDataset articles
29 rdf:type schema:ScholarlyArticle
30 N17518c2b82ff4ec684882a75b37a88c2 schema:affiliation https://www.grid.ac/institutes/grid.410445.0
31 schema:familyName Mookini
32 schema:givenName E. H.
33 rdf:type schema:Person
34 N44547335b8174e6bac483927cc84fc18 schema:name Department of Mathematics, California State College, San Bernardino, California
35 rdf:type schema:Organization
36 N44ca2f585c414a1f806986de6731fae6 schema:name doi
37 schema:value 10.1007/bf00935624
38 rdf:type schema:PropertyValue
39 N47c9e70673284d48ac707ef7185f0cee rdf:first sg:person.013111541222.37
40 rdf:rest N49686c20e4e247628883552a6537dca5
41 N49686c20e4e247628883552a6537dca5 rdf:first N17518c2b82ff4ec684882a75b37a88c2
42 rdf:rest rdf:nil
43 N8ef40ea37c5b4c7b818f207a9b3ef714 schema:issueNumber 1-2
44 rdf:type schema:PublicationIssue
45 Nb6bcbcab55f64d86971e9cc3655af56c schema:name readcube_id
46 schema:value 4619247bc5f7f4d9919679983b75bab795a27d09ee529f6f504dee6a69f16297
47 rdf:type schema:PropertyValue
48 Ncc9aeadafa29498e8923bb9e19040f39 schema:volumeNumber 16
49 rdf:type schema:PublicationVolume
50 Nd93ea7a53b064570b94180f6f6345db3 schema:name Springer Nature - SN SciGraph project
51 rdf:type schema:Organization
52 Ndee3f030d71c499d991e3a1918363cc5 schema:name dimensions_id
53 schema:value pub.1014713541
54 rdf:type schema:PropertyValue
55 anzsrc-for:11 schema:inDefinedTermSet anzsrc-for:
56 schema:name Medical and Health Sciences
57 rdf:type schema:DefinedTerm
58 anzsrc-for:1109 schema:inDefinedTermSet anzsrc-for:
59 schema:name Neurosciences
60 rdf:type schema:DefinedTerm
61 sg:journal.1044187 schema:issn 0022-3239
62 1573-2878
63 schema:name Journal of Optimization Theory and Applications
64 rdf:type schema:Periodical
65 sg:person.013111541222.37 schema:affiliation N44547335b8174e6bac483927cc84fc18
66 schema:familyName Dennemeyer
67 schema:givenName R. F.
68 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013111541222.37
69 rdf:type schema:Person
70 https://doi.org/10.1093/comjnl/6.2.163 schema:sameAs https://app.dimensions.ai/details/publication/pub.1018099115
71 rdf:type schema:CreativeWork
72 https://doi.org/10.1093/comjnl/9.1.67 schema:sameAs https://app.dimensions.ai/details/publication/pub.1005173175
73 rdf:type schema:CreativeWork
74 https://doi.org/10.6028/jres.049.044 schema:sameAs https://app.dimensions.ai/details/publication/pub.1073597164
75 rdf:type schema:CreativeWork
76 https://www.grid.ac/institutes/grid.410445.0 schema:alternateName University of Hawaii at Manoa
77 schema:name Department of Mathematics, University of Hawaii, Honolulu, Hawaii
78 rdf:type schema:Organization
 




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


...