A Numerical Study of Active-Set and Interior-Point Methods for Bound Constrained Optimization View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2008

AUTHORS

Long Hei , Jorge Nocedal , Richard A. Waltz

ABSTRACT

This papers studies the performance of several interior-point and active-set methods on bound constrained optimization problems. The numerical tests show that the sequential linear-quadratic programming (SLQP) method is robust, but is not as effective as gradient projection at identifying the optimal active set. Interior-point methods are robust and require a small number of iterations and function evaluations to converge. An analysis of computing times reveals that it is essential to develop improved preconditioners for the conjugate gradient iterations used in SLQP and interior-point methods. The paper discusses how to efficiently implement incomplete Cholesky preconditioners and how to eliminate ill-conditioning caused by the barrier approach. The paper concludes with an evaluation of methods that use quasi-Newton approximations to the Hessian of the Lagrangian. More... »

PAGES

273-292

References to SciGraph publications

Book

TITLE

Modeling, Simulation and Optimization of Complex Processes

ISBN

978-3-540-79408-0
978-3-540-79409-7

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-540-79409-7_18

DOI

http://dx.doi.org/10.1007/978-3-540-79409-7_18

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1009553625


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/2008/0103", 
        "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/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Northwestern University", 
          "id": "https://www.grid.ac/institutes/grid.16753.36", 
          "name": [
            "Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL\u00a060208, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Hei", 
        "givenName": "Long", 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Northwestern University", 
          "id": "https://www.grid.ac/institutes/grid.16753.36", 
          "name": [
            "Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL\u00a060208, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Nocedal", 
        "givenName": "Jorge", 
        "id": "sg:person.01157306714.71", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01157306714.71"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Northwestern University", 
          "id": "https://www.grid.ac/institutes/grid.16753.36", 
          "name": [
            "Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL\u00a060208, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Waltz", 
        "givenName": "Richard A.", 
        "id": "sg:person.015475525235.83", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015475525235.83"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "https://doi.org/10.1145/279232.279236", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1006445520"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s101070100263", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1040788378", 
          "https://doi.org/10.1007/s101070100263"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1145/962437.962439", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1041348218"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1137/0720042", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1062852930"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1137/0916069", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1062857767"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1137/s0895479899351805", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1062882475"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1137/s1052623497325107", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1062883626"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1137/s1052623498345075", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1062883692"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1137/s1052623499350013", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1062883704"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1137/s1064827597327334", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1062884573"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2008", 
    "datePublishedReg": "2008-01-01", 
    "description": "This papers studies the performance of several interior-point and active-set methods on bound constrained optimization problems. The numerical tests show that the sequential linear-quadratic programming (SLQP) method is robust, but is not as effective as gradient projection at identifying the optimal active set. Interior-point methods are robust and require a small number of iterations and function evaluations to converge. An analysis of computing times reveals that it is essential to develop improved preconditioners for the conjugate gradient iterations used in SLQP and interior-point methods. The paper discusses how to efficiently implement incomplete Cholesky preconditioners and how to eliminate ill-conditioning caused by the barrier approach. The paper concludes with an evaluation of methods that use quasi-Newton approximations to the Hessian of the Lagrangian.", 
    "editor": [
      {
        "familyName": "Bock", 
        "givenName": "Hans Georg", 
        "type": "Person"
      }, 
      {
        "familyName": "Kostina", 
        "givenName": "Ekaterina", 
        "type": "Person"
      }, 
      {
        "familyName": "Phu", 
        "givenName": "Hoang Xuan", 
        "type": "Person"
      }, 
      {
        "familyName": "Rannacher", 
        "givenName": "Rolf", 
        "type": "Person"
      }
    ], 
    "genre": "chapter", 
    "id": "sg:pub.10.1007/978-3-540-79409-7_18", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": true, 
    "isPartOf": {
      "isbn": [
        "978-3-540-79408-0", 
        "978-3-540-79409-7"
      ], 
      "name": "Modeling, Simulation and Optimization of Complex Processes", 
      "type": "Book"
    }, 
    "name": "A Numerical Study of Active-Set and Interior-Point Methods for Bound Constrained Optimization", 
    "pagination": "273-292", 
    "productId": [
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/978-3-540-79409-7_18"
        ]
      }, 
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "2d8297f53df9087a9205ecdd32c0d2d8e9986422d130acfe4990cdcf5dddb638"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1009553625"
        ]
      }
    ], 
    "publisher": {
      "location": "Berlin, Heidelberg", 
      "name": "Springer Berlin Heidelberg", 
      "type": "Organisation"
    }, 
    "sameAs": [
      "https://doi.org/10.1007/978-3-540-79409-7_18", 
      "https://app.dimensions.ai/details/publication/pub.1009553625"
    ], 
    "sdDataset": "chapters", 
    "sdDatePublished": "2019-04-15T11:32", 
    "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_8660_00000249.jsonl", 
    "type": "Chapter", 
    "url": "http://link.springer.com/10.1007/978-3-540-79409-7_18"
  }
]
 

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.10.1007/978-3-540-79409-7_18'

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

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-3-540-79409-7_18'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-3-540-79409-7_18'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-3-540-79409-7_18'


 

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

125 TRIPLES      23 PREDICATES      37 URIs      20 LITERALS      8 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/978-3-540-79409-7_18 schema:about anzsrc-for:01
2 anzsrc-for:0103
3 schema:author Ne5adee2787fc4954a4e852dc0ac236cb
4 schema:citation sg:pub.10.1007/s101070100263
5 https://doi.org/10.1137/0720042
6 https://doi.org/10.1137/0916069
7 https://doi.org/10.1137/s0895479899351805
8 https://doi.org/10.1137/s1052623497325107
9 https://doi.org/10.1137/s1052623498345075
10 https://doi.org/10.1137/s1052623499350013
11 https://doi.org/10.1137/s1064827597327334
12 https://doi.org/10.1145/279232.279236
13 https://doi.org/10.1145/962437.962439
14 schema:datePublished 2008
15 schema:datePublishedReg 2008-01-01
16 schema:description This papers studies the performance of several interior-point and active-set methods on bound constrained optimization problems. The numerical tests show that the sequential linear-quadratic programming (SLQP) method is robust, but is not as effective as gradient projection at identifying the optimal active set. Interior-point methods are robust and require a small number of iterations and function evaluations to converge. An analysis of computing times reveals that it is essential to develop improved preconditioners for the conjugate gradient iterations used in SLQP and interior-point methods. The paper discusses how to efficiently implement incomplete Cholesky preconditioners and how to eliminate ill-conditioning caused by the barrier approach. The paper concludes with an evaluation of methods that use quasi-Newton approximations to the Hessian of the Lagrangian.
17 schema:editor N2ba721aac8664e46827531aa05c6fb5f
18 schema:genre chapter
19 schema:inLanguage en
20 schema:isAccessibleForFree true
21 schema:isPartOf N9f6e24172ca44562930020c2c7fe74c1
22 schema:name A Numerical Study of Active-Set and Interior-Point Methods for Bound Constrained Optimization
23 schema:pagination 273-292
24 schema:productId N017aa1b8bfee4f84bfada8adfe43bbe7
25 N578dbba38a4b4c7894c984a7ba836e86
26 Nc6775824712f4e45809d873636fd8eef
27 schema:publisher N5884d46a4552427597439786e9cf6157
28 schema:sameAs https://app.dimensions.ai/details/publication/pub.1009553625
29 https://doi.org/10.1007/978-3-540-79409-7_18
30 schema:sdDatePublished 2019-04-15T11:32
31 schema:sdLicense https://scigraph.springernature.com/explorer/license/
32 schema:sdPublisher N3b5782548b0643519d36421170034593
33 schema:url http://link.springer.com/10.1007/978-3-540-79409-7_18
34 sgo:license sg:explorer/license/
35 sgo:sdDataset chapters
36 rdf:type schema:Chapter
37 N017aa1b8bfee4f84bfada8adfe43bbe7 schema:name readcube_id
38 schema:value 2d8297f53df9087a9205ecdd32c0d2d8e9986422d130acfe4990cdcf5dddb638
39 rdf:type schema:PropertyValue
40 N11b6ec877a0241b78d32f96c96a369bc rdf:first sg:person.015475525235.83
41 rdf:rest rdf:nil
42 N14db95fa9969468893e733bb7e51fc81 schema:familyName Bock
43 schema:givenName Hans Georg
44 rdf:type schema:Person
45 N2ba721aac8664e46827531aa05c6fb5f rdf:first N14db95fa9969468893e733bb7e51fc81
46 rdf:rest N86be047028854eb19b39693f7bc8fb19
47 N2ecf760b7eab4755bb04da9a12a2001f schema:familyName Kostina
48 schema:givenName Ekaterina
49 rdf:type schema:Person
50 N3b5782548b0643519d36421170034593 schema:name Springer Nature - SN SciGraph project
51 rdf:type schema:Organization
52 N4388679a8072413792ec28c57df7b277 rdf:first sg:person.01157306714.71
53 rdf:rest N11b6ec877a0241b78d32f96c96a369bc
54 N578dbba38a4b4c7894c984a7ba836e86 schema:name dimensions_id
55 schema:value pub.1009553625
56 rdf:type schema:PropertyValue
57 N5884d46a4552427597439786e9cf6157 schema:location Berlin, Heidelberg
58 schema:name Springer Berlin Heidelberg
59 rdf:type schema:Organisation
60 N661d825f8f04414daabfc12a097bfc8f schema:familyName Phu
61 schema:givenName Hoang Xuan
62 rdf:type schema:Person
63 N66e73991ace14df9a4690c6a7b9cb062 schema:affiliation https://www.grid.ac/institutes/grid.16753.36
64 schema:familyName Hei
65 schema:givenName Long
66 rdf:type schema:Person
67 N754eda397b0a4094a77e940a3ef48fe9 schema:familyName Rannacher
68 schema:givenName Rolf
69 rdf:type schema:Person
70 N7cf6e671ab864edd9622df081894a8da rdf:first N754eda397b0a4094a77e940a3ef48fe9
71 rdf:rest rdf:nil
72 N86be047028854eb19b39693f7bc8fb19 rdf:first N2ecf760b7eab4755bb04da9a12a2001f
73 rdf:rest Nf34642bb31324df48ec259903772194b
74 N9f6e24172ca44562930020c2c7fe74c1 schema:isbn 978-3-540-79408-0
75 978-3-540-79409-7
76 schema:name Modeling, Simulation and Optimization of Complex Processes
77 rdf:type schema:Book
78 Nc6775824712f4e45809d873636fd8eef schema:name doi
79 schema:value 10.1007/978-3-540-79409-7_18
80 rdf:type schema:PropertyValue
81 Ne5adee2787fc4954a4e852dc0ac236cb rdf:first N66e73991ace14df9a4690c6a7b9cb062
82 rdf:rest N4388679a8072413792ec28c57df7b277
83 Nf34642bb31324df48ec259903772194b rdf:first N661d825f8f04414daabfc12a097bfc8f
84 rdf:rest N7cf6e671ab864edd9622df081894a8da
85 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
86 schema:name Mathematical Sciences
87 rdf:type schema:DefinedTerm
88 anzsrc-for:0103 schema:inDefinedTermSet anzsrc-for:
89 schema:name Numerical and Computational Mathematics
90 rdf:type schema:DefinedTerm
91 sg:person.01157306714.71 schema:affiliation https://www.grid.ac/institutes/grid.16753.36
92 schema:familyName Nocedal
93 schema:givenName Jorge
94 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01157306714.71
95 rdf:type schema:Person
96 sg:person.015475525235.83 schema:affiliation https://www.grid.ac/institutes/grid.16753.36
97 schema:familyName Waltz
98 schema:givenName Richard A.
99 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015475525235.83
100 rdf:type schema:Person
101 sg:pub.10.1007/s101070100263 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040788378
102 https://doi.org/10.1007/s101070100263
103 rdf:type schema:CreativeWork
104 https://doi.org/10.1137/0720042 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062852930
105 rdf:type schema:CreativeWork
106 https://doi.org/10.1137/0916069 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062857767
107 rdf:type schema:CreativeWork
108 https://doi.org/10.1137/s0895479899351805 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062882475
109 rdf:type schema:CreativeWork
110 https://doi.org/10.1137/s1052623497325107 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062883626
111 rdf:type schema:CreativeWork
112 https://doi.org/10.1137/s1052623498345075 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062883692
113 rdf:type schema:CreativeWork
114 https://doi.org/10.1137/s1052623499350013 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062883704
115 rdf:type schema:CreativeWork
116 https://doi.org/10.1137/s1064827597327334 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062884573
117 rdf:type schema:CreativeWork
118 https://doi.org/10.1145/279232.279236 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006445520
119 rdf:type schema:CreativeWork
120 https://doi.org/10.1145/962437.962439 schema:sameAs https://app.dimensions.ai/details/publication/pub.1041348218
121 rdf:type schema:CreativeWork
122 https://www.grid.ac/institutes/grid.16753.36 schema:alternateName Northwestern University
123 schema:name Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL 60208, USA
124 Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL 60208, USA
125 rdf:type schema:Organization
 




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


...