Matrix conditioning and nonlinear optimization View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1978-12

AUTHORS

D. F. Shanno, Kang -Hoh Phua

ABSTRACT

In a series of recent papers, Oren, Oren and Luenberger, Oren and Spedicato, and Spedicato have developed the self-scaling variable metric algorithms. These algorithms alter Broyden's single parameter family of approximations to the inverse Hessian to a double parameter family. Conditions are given on the new parameter to minimize a bound on the condition number of the approximated inverse Hessian while insuring improved step-wise convergence. Davidon has devised an update which also minimizes the bound on the condition number while remaining in the Broyden single parameter family. This paper derives initial scalings for the approximate inverse Hessian which makes members of the Broyden class self-scaling. The Davidon, BFGS, and Oren—Spedicato updates are tested for computational efficiency and stability on numerous test functions, with the results indicating strong superiority computationally for the Davidon and BFGS update over the self-scaling update, except on a special class of functions, the homogeneous functions. More... »

PAGES

149-160

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf01588962

DOI

http://dx.doi.org/10.1007/bf01588962

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1048725219


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/2008/0801", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Artificial Intelligence and Image Processing", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/08", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Information and Computing Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "University of Arizona", 
          "id": "https://www.grid.ac/institutes/grid.134563.6", 
          "name": [
            "The University of Arizona, Tucson, AZ, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Shanno", 
        "givenName": "D. F.", 
        "id": "sg:person.016556335135.48", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016556335135.48"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "National University of Singapore", 
          "id": "https://www.grid.ac/institutes/grid.4280.e", 
          "name": [
            "Nanyang University, Singapore"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Phua", 
        "givenName": "Kang -Hoh", 
        "id": "sg:person.016703443314.24", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016703443314.24"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "https://doi.org/10.1090/s0025-5718-1970-0274029-x", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1000595399"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/s0025-5718-1967-0224273-2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1004629228"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/s0025-5718-1970-0258249-6", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1004777117"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1093/comjnl/13.3.317", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1007597686"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01585530", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1008457144", 
          "https://doi.org/10.1007/bf01585530"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01584978", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1020745245", 
          "https://doi.org/10.1007/bf01584978"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01681328", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1020786346", 
          "https://doi.org/10.1007/bf01681328"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01681328", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1020786346", 
          "https://doi.org/10.1007/bf01681328"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1145/355666.355673", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1031990576"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01580654", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1040008409", 
          "https://doi.org/10.1007/bf01580654"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1093/imamat/6.3.222", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1059685647"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1287/mnsc.20.5.845", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064717375"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1287/mnsc.20.5.863", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064717376"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "1978-12", 
    "datePublishedReg": "1978-12-01", 
    "description": "In a series of recent papers, Oren, Oren and Luenberger, Oren and Spedicato, and Spedicato have developed the self-scaling variable metric algorithms. These algorithms alter Broyden's single parameter family of approximations to the inverse Hessian to a double parameter family. Conditions are given on the new parameter to minimize a bound on the condition number of the approximated inverse Hessian while insuring improved step-wise convergence. Davidon has devised an update which also minimizes the bound on the condition number while remaining in the Broyden single parameter family. This paper derives initial scalings for the approximate inverse Hessian which makes members of the Broyden class self-scaling. The Davidon, BFGS, and Oren\u2014Spedicato updates are tested for computational efficiency and stability on numerous test functions, with the results indicating strong superiority computationally for the Davidon and BFGS update over the self-scaling update, except on a special class of functions, the homogeneous functions.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/bf01588962", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1047630", 
        "issn": [
          "0025-5610", 
          "1436-4646"
        ], 
        "name": "Mathematical Programming", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "1", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "14"
      }
    ], 
    "name": "Matrix conditioning and nonlinear optimization", 
    "pagination": "149-160", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "e81e35450b21b93005ce356bdd70cb1a21009aac86b5a5ba73ac0ff2a20bbc24"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/bf01588962"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1048725219"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/bf01588962", 
      "https://app.dimensions.ai/details/publication/pub.1048725219"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-10T20:58", 
    "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/v90/0000000001_0000000264/records_8684_00000594.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "http://link.springer.com/10.1007%2FBF01588962"
  }
]
 

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/bf01588962'

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/bf01588962'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/bf01588962'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/bf01588962'


 

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

111 TRIPLES      21 PREDICATES      39 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/bf01588962 schema:about anzsrc-for:08
2 anzsrc-for:0801
3 schema:author N7ef5349c39454c5a8eb052547c7451dd
4 schema:citation sg:pub.10.1007/bf01580654
5 sg:pub.10.1007/bf01584978
6 sg:pub.10.1007/bf01585530
7 sg:pub.10.1007/bf01681328
8 https://doi.org/10.1090/s0025-5718-1967-0224273-2
9 https://doi.org/10.1090/s0025-5718-1970-0258249-6
10 https://doi.org/10.1090/s0025-5718-1970-0274029-x
11 https://doi.org/10.1093/comjnl/13.3.317
12 https://doi.org/10.1093/imamat/6.3.222
13 https://doi.org/10.1145/355666.355673
14 https://doi.org/10.1287/mnsc.20.5.845
15 https://doi.org/10.1287/mnsc.20.5.863
16 schema:datePublished 1978-12
17 schema:datePublishedReg 1978-12-01
18 schema:description In a series of recent papers, Oren, Oren and Luenberger, Oren and Spedicato, and Spedicato have developed the self-scaling variable metric algorithms. These algorithms alter Broyden's single parameter family of approximations to the inverse Hessian to a double parameter family. Conditions are given on the new parameter to minimize a bound on the condition number of the approximated inverse Hessian while insuring improved step-wise convergence. Davidon has devised an update which also minimizes the bound on the condition number while remaining in the Broyden single parameter family. This paper derives initial scalings for the approximate inverse Hessian which makes members of the Broyden class self-scaling. The Davidon, BFGS, and Oren—Spedicato updates are tested for computational efficiency and stability on numerous test functions, with the results indicating strong superiority computationally for the Davidon and BFGS update over the self-scaling update, except on a special class of functions, the homogeneous functions.
19 schema:genre research_article
20 schema:inLanguage en
21 schema:isAccessibleForFree false
22 schema:isPartOf N393b7f32832d4c9abf6eae2a52c1a241
23 Nc5a398253b3e4fe58bd8e5095ef7ab4c
24 sg:journal.1047630
25 schema:name Matrix conditioning and nonlinear optimization
26 schema:pagination 149-160
27 schema:productId N8ae03a62a26f4358b91a513881327f78
28 N965f6373705746558f7789156d954a56
29 Ncb7e5e91ea4e41ada5bcf45878109332
30 schema:sameAs https://app.dimensions.ai/details/publication/pub.1048725219
31 https://doi.org/10.1007/bf01588962
32 schema:sdDatePublished 2019-04-10T20:58
33 schema:sdLicense https://scigraph.springernature.com/explorer/license/
34 schema:sdPublisher N2632e14e79ef4bc48e92268a89b5a078
35 schema:url http://link.springer.com/10.1007%2FBF01588962
36 sgo:license sg:explorer/license/
37 sgo:sdDataset articles
38 rdf:type schema:ScholarlyArticle
39 N2632e14e79ef4bc48e92268a89b5a078 schema:name Springer Nature - SN SciGraph project
40 rdf:type schema:Organization
41 N393b7f32832d4c9abf6eae2a52c1a241 schema:issueNumber 1
42 rdf:type schema:PublicationIssue
43 N40bc675b48154aef818f33353cd590a9 rdf:first sg:person.016703443314.24
44 rdf:rest rdf:nil
45 N7ef5349c39454c5a8eb052547c7451dd rdf:first sg:person.016556335135.48
46 rdf:rest N40bc675b48154aef818f33353cd590a9
47 N8ae03a62a26f4358b91a513881327f78 schema:name dimensions_id
48 schema:value pub.1048725219
49 rdf:type schema:PropertyValue
50 N965f6373705746558f7789156d954a56 schema:name doi
51 schema:value 10.1007/bf01588962
52 rdf:type schema:PropertyValue
53 Nc5a398253b3e4fe58bd8e5095ef7ab4c schema:volumeNumber 14
54 rdf:type schema:PublicationVolume
55 Ncb7e5e91ea4e41ada5bcf45878109332 schema:name readcube_id
56 schema:value e81e35450b21b93005ce356bdd70cb1a21009aac86b5a5ba73ac0ff2a20bbc24
57 rdf:type schema:PropertyValue
58 anzsrc-for:08 schema:inDefinedTermSet anzsrc-for:
59 schema:name Information and Computing Sciences
60 rdf:type schema:DefinedTerm
61 anzsrc-for:0801 schema:inDefinedTermSet anzsrc-for:
62 schema:name Artificial Intelligence and Image Processing
63 rdf:type schema:DefinedTerm
64 sg:journal.1047630 schema:issn 0025-5610
65 1436-4646
66 schema:name Mathematical Programming
67 rdf:type schema:Periodical
68 sg:person.016556335135.48 schema:affiliation https://www.grid.ac/institutes/grid.134563.6
69 schema:familyName Shanno
70 schema:givenName D. F.
71 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016556335135.48
72 rdf:type schema:Person
73 sg:person.016703443314.24 schema:affiliation https://www.grid.ac/institutes/grid.4280.e
74 schema:familyName Phua
75 schema:givenName Kang -Hoh
76 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016703443314.24
77 rdf:type schema:Person
78 sg:pub.10.1007/bf01580654 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040008409
79 https://doi.org/10.1007/bf01580654
80 rdf:type schema:CreativeWork
81 sg:pub.10.1007/bf01584978 schema:sameAs https://app.dimensions.ai/details/publication/pub.1020745245
82 https://doi.org/10.1007/bf01584978
83 rdf:type schema:CreativeWork
84 sg:pub.10.1007/bf01585530 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008457144
85 https://doi.org/10.1007/bf01585530
86 rdf:type schema:CreativeWork
87 sg:pub.10.1007/bf01681328 schema:sameAs https://app.dimensions.ai/details/publication/pub.1020786346
88 https://doi.org/10.1007/bf01681328
89 rdf:type schema:CreativeWork
90 https://doi.org/10.1090/s0025-5718-1967-0224273-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004629228
91 rdf:type schema:CreativeWork
92 https://doi.org/10.1090/s0025-5718-1970-0258249-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004777117
93 rdf:type schema:CreativeWork
94 https://doi.org/10.1090/s0025-5718-1970-0274029-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1000595399
95 rdf:type schema:CreativeWork
96 https://doi.org/10.1093/comjnl/13.3.317 schema:sameAs https://app.dimensions.ai/details/publication/pub.1007597686
97 rdf:type schema:CreativeWork
98 https://doi.org/10.1093/imamat/6.3.222 schema:sameAs https://app.dimensions.ai/details/publication/pub.1059685647
99 rdf:type schema:CreativeWork
100 https://doi.org/10.1145/355666.355673 schema:sameAs https://app.dimensions.ai/details/publication/pub.1031990576
101 rdf:type schema:CreativeWork
102 https://doi.org/10.1287/mnsc.20.5.845 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064717375
103 rdf:type schema:CreativeWork
104 https://doi.org/10.1287/mnsc.20.5.863 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064717376
105 rdf:type schema:CreativeWork
106 https://www.grid.ac/institutes/grid.134563.6 schema:alternateName University of Arizona
107 schema:name The University of Arizona, Tucson, AZ, USA
108 rdf:type schema:Organization
109 https://www.grid.ac/institutes/grid.4280.e schema:alternateName National University of Singapore
110 schema:name Nanyang University, Singapore
111 rdf:type schema:Organization
 




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


...