schliessen

Filtern

 

Bibliotheken

An inexact dual logarithmic barrier method for solving sparse semidefinite programs

A dual logarithmic barrier method for solving large, sparse semidefinite programs is proposed in this paper. The method avoids any explicit use of the primal variable X and therefore is well-suited to problems with a sparse dual matrix S . It relies on inexact Newton steps in dual space which are co... Full description

Journal Title: Mathematical programming 2018-04-28, Vol.178 (1-2), p.109-143
Main Author: Bellavia, Stefania
Other Authors: Gondzio, Jacek , Porcelli, Margherita
Format: Electronic Article Electronic Article
Language: English
Subjects:
Publisher: Berlin/Heidelberg: Springer Berlin Heidelberg
ID: ISSN: 0025-5610
Zum Text:
SendSend as email Add to Book BagAdd to Book Bag
Staff View
recordid: cdi_proquest_journals_2306807895
title: An inexact dual logarithmic barrier method for solving sparse semidefinite programs
format: Article
creator:
  • Bellavia, Stefania
  • Gondzio, Jacek
  • Porcelli, Margherita
subjects:
  • Algorithms
  • Calculus of Variations and Optimal Control
  • Optimization
  • Cholesky factorization
  • Combinatorics
  • Complement
  • Conjugate gradient method
  • Dual logarithmic barrier method
  • Full Length Paper
  • Inexact Newton method
  • Iterative methods
  • Mathematical analysis
  • Mathematical and Computational Physics
  • Mathematical Methods in Physics
  • Mathematics
  • Mathematics and Statistics
  • Mathematics of Computing
  • Matrix algebra
  • Matrix methods
  • Methods
  • Numerical Analysis
  • Optimization
  • Polynomials
  • Preconditioning
  • Semidefinite programming
  • Sparsity
  • Theoretical
ispartof: Mathematical programming, 2018-04-28, Vol.178 (1-2), p.109-143
description: A dual logarithmic barrier method for solving large, sparse semidefinite programs is proposed in this paper. The method avoids any explicit use of the primal variable X and therefore is well-suited to problems with a sparse dual matrix S . It relies on inexact Newton steps in dual space which are computed by the conjugate gradient method applied to the Schur complement of the reduced KKT system. The method may take advantage of low-rank representations of matrices A i to perform implicit matrix-vector products with the Schur complement matrix and to compute only specific parts of this matrix. This allows the construction of the partial Cholesky factorization of the Schur complement matrix which serves as a good preconditioner for it and permits the method to be run in a matrix-free scheme. Convergence properties of the method are studied and a polynomial complexity result is extended to the case when inexact Newton steps are employed. A Matlab-based implementation is developed and preliminary computational results of applying the method to maximum cut and matrix completion problems are reported.
language: eng
source:
identifier: ISSN: 0025-5610
fulltext: no_fulltext
issn:
  • 0025-5610
  • 1436-4646
url: Link


@attributes
NO1
SEARCH_ENGINEprimo_central_multiple_fe
SEARCH_ENGINE_TYPEPrimo Central Search Engine
RANK2.5616884
LOCALfalse
PrimoNMBib
record
control
sourceidgale_opena
recordidTN_cdi_proquest_journals_2306807895
sourceformatXML
sourcesystemPC
galeidA603161063
sourcerecordidA603161063
originalsourceidFETCH-LOGICAL-c458t-9d421965b5db2ce5f863c9ab9a06d660d909e56902add28b00b1b667138386bf0
addsrcrecordideNqNUk2LFDEUDKLgOPoDvAU89_ry2clxWNRdWNiDeg7pTtKbpTsZkx7Rf2-aFj25yDsEHlVFvUoh9JbAFQHo31cCBPoOiOoIVaQTz9CBcCY7Lrl8jg4AVHRCEniJXtX6CACEKXVAn08Jx-R_2HHF7mJnPOfJlrg-LHHEgy0l-oIXvz5kh0MuuOb5e0wTrmdbqsfVL9H5EFNcPT6XPBW71NfoRbBz9W9-v0f09eOHL9c33d39p9vr0103cqHWTjtOiZZiEG6goxdBSTZqO2gL0kkJToP2Qmqg1jmqBoCBDFL2zThTcghwRLe7bj77ZGPx5lziYstPk200LvnVZGc4aG4U0N5RqwLXTlHNgtfC9ZoH6rmTXP2nFtu0mB0EFZbLXlhHqfVaBTcSxRUBFto3HNG7XasF8u3i62oe86WkFoWhDKSCXmnxJAoYkZQD4Q11taMmO3sTU8hrsWMb15Ifc2rZt_1JbgwCkjUC2QljybUWH_4cQsBsVTF7VUyritmqYjYrdOfUhk2TL3-t_Jv0Cyn5vGA
sourcetypeOpen Access Repository
isCDItrue
recordtypearticle
pqid2031624014
display
typearticle
titleAn inexact dual logarithmic barrier method for solving sparse semidefinite programs
creatorBellavia, Stefania ; Gondzio, Jacek ; Porcelli, Margherita
creatorcontribBellavia, Stefania ; Gondzio, Jacek ; Porcelli, Margherita
descriptionA dual logarithmic barrier method for solving large, sparse semidefinite programs is proposed in this paper. The method avoids any explicit use of the primal variable X and therefore is well-suited to problems with a sparse dual matrix S . It relies on inexact Newton steps in dual space which are computed by the conjugate gradient method applied to the Schur complement of the reduced KKT system. The method may take advantage of low-rank representations of matrices A i to perform implicit matrix-vector products with the Schur complement matrix and to compute only specific parts of this matrix. This allows the construction of the partial Cholesky factorization of the Schur complement matrix which serves as a good preconditioner for it and permits the method to be run in a matrix-free scheme. Convergence properties of the method are studied and a polynomial complexity result is extended to the case when inexact Newton steps are employed. A Matlab-based implementation is developed and preliminary computational results of applying the method to maximum cut and matrix completion problems are reported.
identifier
0ISSN: 0025-5610
1EISSN: 1436-4646
2DOI: 10.1007/s10107-018-1281-5
languageeng
publisherBerlin/Heidelberg: Springer Berlin Heidelberg
subjectAlgorithms ; Calculus of Variations and Optimal Control; Optimization ; Cholesky factorization ; Combinatorics ; Complement ; Conjugate gradient method ; Dual logarithmic barrier method ; Full Length Paper ; Inexact Newton method ; Iterative methods ; Mathematical analysis ; Mathematical and Computational Physics ; Mathematical Methods in Physics ; Mathematics ; Mathematics and Statistics ; Mathematics of Computing ; Matrix algebra ; Matrix methods ; Methods ; Numerical Analysis ; Optimization ; Polynomials ; Preconditioning ; Semidefinite programming ; Sparsity ; Theoretical
ispartofMathematical programming, 2018-04-28, Vol.178 (1-2), p.109-143
rights
0Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2018
1COPYRIGHT 2019 Springer
2Mathematical Programming is a copyright of Springer, (2018). All Rights Reserved.
3Copyright Springer Nature B.V. 2019
lds50peer_reviewed
oafree_for_read
citesFETCH-LOGICAL-c458t-9d421965b5db2ce5f863c9ab9a06d660d909e56902add28b00b1b667138386bf0
orcidid0000-0003-0183-1204
links
openurl$$Topenurl_article
thumbnail$$Usyndetics_thumb_exl
search
creatorcontrib
0Bellavia, Stefania
1Gondzio, Jacek
2Porcelli, Margherita
title
0An inexact dual logarithmic barrier method for solving sparse semidefinite programs
1Mathematical programming
addtitleMath. Program
descriptionA dual logarithmic barrier method for solving large, sparse semidefinite programs is proposed in this paper. The method avoids any explicit use of the primal variable X and therefore is well-suited to problems with a sparse dual matrix S . It relies on inexact Newton steps in dual space which are computed by the conjugate gradient method applied to the Schur complement of the reduced KKT system. The method may take advantage of low-rank representations of matrices A i to perform implicit matrix-vector products with the Schur complement matrix and to compute only specific parts of this matrix. This allows the construction of the partial Cholesky factorization of the Schur complement matrix which serves as a good preconditioner for it and permits the method to be run in a matrix-free scheme. Convergence properties of the method are studied and a polynomial complexity result is extended to the case when inexact Newton steps are employed. A Matlab-based implementation is developed and preliminary computational results of applying the method to maximum cut and matrix completion problems are reported.
subject
0Algorithms
1Calculus of Variations and Optimal Control; Optimization
2Cholesky factorization
3Combinatorics
4Complement
5Conjugate gradient method
6Dual logarithmic barrier method
7Full Length Paper
8Inexact Newton method
9Iterative methods
10Mathematical analysis
11Mathematical and Computational Physics
12Mathematical Methods in Physics
13Mathematics
14Mathematics and Statistics
15Mathematics of Computing
16Matrix algebra
17Matrix methods
18Methods
19Numerical Analysis
20Optimization
21Polynomials
22Preconditioning
23Semidefinite programming
24Sparsity
25Theoretical
issn
00025-5610
11436-4646
fulltextfalse
rsrctypearticle
creationdate2018
recordtypearticle
recordideNqNUk2LFDEUDKLgOPoDvAU89_ry2clxWNRdWNiDeg7pTtKbpTsZkx7Rf2-aFj25yDsEHlVFvUoh9JbAFQHo31cCBPoOiOoIVaQTz9CBcCY7Lrl8jg4AVHRCEniJXtX6CACEKXVAn08Jx-R_2HHF7mJnPOfJlrg-LHHEgy0l-oIXvz5kh0MuuOb5e0wTrmdbqsfVL9H5EFNcPT6XPBW71NfoRbBz9W9-v0f09eOHL9c33d39p9vr0103cqHWTjtOiZZiEG6goxdBSTZqO2gL0kkJToP2Qmqg1jmqBoCBDFL2zThTcghwRLe7bj77ZGPx5lziYstPk200LvnVZGc4aG4U0N5RqwLXTlHNgtfC9ZoH6rmTXP2nFtu0mB0EFZbLXlhHqfVaBTcSxRUBFto3HNG7XasF8u3i62oe86WkFoWhDKSCXmnxJAoYkZQD4Q11taMmO3sTU8hrsWMb15Ifc2rZt_1JbgwCkjUC2QljybUWH_4cQsBsVTF7VUyritmqYjYrdOfUhk2TL3-t_Jv0Cyn5vGA
startdate20180428
enddate20180428
creator
0Bellavia, Stefania
1Gondzio, Jacek
2Porcelli, Margherita
general
0Springer Berlin Heidelberg
1Springer
2Springer Nature B.V
scope
0AAYXX
1CITATION
2BSHEE
33V.
47SC
57WY
67WZ
77XB
887Z
988I
108AL
118AO
128FD
138FE
148FG
158FK
168FL
17ABJCF
18ABUWG
19ARAPS
20AZQEC
21BENPR
22BEZIV
23BGLVJ
24DWQXO
25FRNLG
26F~G
27GNUQQ
28HCIFZ
29JQ2
30K60
31K6~
32K7-
33L.-
34L6V
35L7M
36L~C
37L~D
38M0C
39M0N
40M2P
41M7S
42P5Z
43P62
44PQBIZ
45PQBZA
46PQEST
47PQQKQ
48PQUKI
49PRINS
50PTHSS
51PYYUZ
52Q9U
53BOBZL
54CLFQK
orcididhttps://orcid.org/0000-0003-0183-1204
sort
creationdate20180428
titleAn inexact dual logarithmic barrier method for solving sparse semidefinite programs
authorBellavia, Stefania ; Gondzio, Jacek ; Porcelli, Margherita
facets
frbrtype5
frbrgroupidcdi_FETCH-LOGICAL-c458t-9d421965b5db2ce5f863c9ab9a06d660d909e56902add28b00b1b667138386bf0
rsrctypearticles
prefilterarticles
languageeng
creationdate2018
topic
0Algorithms
1Calculus of Variations and Optimal Control; Optimization
2Cholesky factorization
3Combinatorics
4Complement
5Conjugate gradient method
6Dual logarithmic barrier method
7Full Length Paper
8Inexact Newton method
9Iterative methods
10Mathematical analysis
11Mathematical and Computational Physics
12Mathematical Methods in Physics
13Mathematics
14Mathematics and Statistics
15Mathematics of Computing
16Matrix algebra
17Matrix methods
18Methods
19Numerical Analysis
20Optimization
21Polynomials
22Preconditioning
23Semidefinite programming
24Sparsity
25Theoretical
toplevelpeer_reviewed
creatorcontrib
0Bellavia, Stefania
1Gondzio, Jacek
2Porcelli, Margherita
collection
0CrossRef
1Academic OneFile (A&I only)
2ProQuest Central (Corporate)
3Computer and Information Systems Abstracts
4ABI/INFORM Collection
5ABI/INFORM Global (PDF only)
6ProQuest Central (purchase pre-March 2016)
7ABI/INFORM Global (Alumni Edition)
8Science Database (Alumni Edition)
9Computing Database (Alumni Edition)
10ProQuest Pharma Collection
11Technology Research Database
12ProQuest SciTech Collection
13ProQuest Technology Collection
14ProQuest Central (Alumni) (purchase pre-March 2016)
15ABI/INFORM Collection (Alumni Edition)
16Materials Science & Engineering Collection
17ProQuest Central (Alumni Edition)
18Advanced Technologies & Aerospace Collection
19ProQuest Central Essentials
20ProQuest Central
21Business Premium Collection
22Technology Collection
23ProQuest Central Korea
24Business Premium Collection (Alumni)
25ABI/INFORM Global (Corporate)
26ProQuest Central Student
27SciTech Premium Collection
28ProQuest Computer Science Collection
29ProQuest Business Collection (Alumni Edition)
30ProQuest Business Collection
31Computer Science Database
32ABI/INFORM Professional Advanced
33ProQuest Engineering Collection
34Advanced Technologies Database with Aerospace
35Computer and Information Systems Abstracts – Academic
36Computer and Information Systems Abstracts Professional
37ABI/INFORM Global
38Computing Database
39Science Database
40Engineering Database
41Advanced Technologies & Aerospace Database
42ProQuest Advanced Technologies & Aerospace Collection
43ProQuest One Business
44ProQuest One Business (Alumni)
45ProQuest One Academic Eastern Edition
46ProQuest One Academic
47ProQuest One Academic UKI Edition
48ProQuest Central China
49Engineering Collection
50ABI/INFORM Collection China
51ProQuest Central Basic
52OpenAIRE (Open Access)
53OpenAIRE
jtitleMathematical programming
delivery
delcategoryRemote Search Resource
fulltextno_fulltext
addata
au
0Bellavia, Stefania
1Gondzio, Jacek
2Porcelli, Margherita
formatjournal
genrearticle
ristypeJOUR
atitleAn inexact dual logarithmic barrier method for solving sparse semidefinite programs
jtitleMathematical programming
stitleMath. Program
date2018-04-28
risdate2018
volume178
issue1-2
spage109
epage143
pages109-143
issn0025-5610
eissn1436-4646
abstractA dual logarithmic barrier method for solving large, sparse semidefinite programs is proposed in this paper. The method avoids any explicit use of the primal variable X and therefore is well-suited to problems with a sparse dual matrix S . It relies on inexact Newton steps in dual space which are computed by the conjugate gradient method applied to the Schur complement of the reduced KKT system. The method may take advantage of low-rank representations of matrices A i to perform implicit matrix-vector products with the Schur complement matrix and to compute only specific parts of this matrix. This allows the construction of the partial Cholesky factorization of the Schur complement matrix which serves as a good preconditioner for it and permits the method to be run in a matrix-free scheme. Convergence properties of the method are studied and a polynomial complexity result is extended to the case when inexact Newton steps are employed. A Matlab-based implementation is developed and preliminary computational results of applying the method to maximum cut and matrix completion problems are reported.
copBerlin/Heidelberg
pubSpringer Berlin Heidelberg
doi10.1007/s10107-018-1281-5
orcididhttps://orcid.org/0000-0003-0183-1204
oafree_for_read