A Benson-type algorithm for bounded convex vector optimization problems with vertex selection

We present an algorithm for approximately solving bounded convex vector optimization problems. The algorithm provides both an outer and an inner polyhedral approximation of the upper image. It is a modification of the primal algorithm presented by Löhne, Rudloff, and Ulus in 2014. There, vertices of...

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Published in:Optimization methods & software Vol. 37; no. 3; pp. 1006 - 1026
Main Authors: Dörfler, Daniel, Löhne, Andreas, Schneider, Christopher, Weißing, Benjamin
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 04.05.2022
Taylor & Francis Ltd
Subjects:
90-08
Algorithms
Apexes
Approximation
convex programming
Mathematical analysis
multiple objective optimization
Optimization
polyhedral approximation
Vector optimization
ISSN:1055-6788, 1029-4937
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Abstract We present an algorithm for approximately solving bounded convex vector optimization problems. The algorithm provides both an outer and an inner polyhedral approximation of the upper image. It is a modification of the primal algorithm presented by Löhne, Rudloff, and Ulus in 2014. There, vertices of an already known outer approximation are successively cutoff to improve the approximation error. We propose a new and efficient selection rule for deciding which vertex to cutoff. Numerical examples are provided which illustrate that this method may solve fewer scalar problems overall and therefore may be faster while achieving the same approximation quality.
AbstractList We present an algorithm for approximately solving bounded convex vector optimization problems. The algorithm provides both an outer and an inner polyhedral approximation of the upper image. It is a modification of the primal algorithm presented by Löhne, Rudloff, and Ulus in 2014. There, vertices of an already known outer approximation are successively cutoff to improve the approximation error. We propose a new and efficient selection rule for deciding which vertex to cutoff. Numerical examples are provided which illustrate that this method may solve fewer scalar problems overall and therefore may be faster while achieving the same approximation quality.
Author Dörfler, Daniel
Löhne, Andreas
Schneider, Christopher
Weißing, Benjamin
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  surname: Dörfler
  fullname: Dörfler, Daniel
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  givenname: Andreas
  surname: Löhne
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  givenname: Christopher
  surname: Schneider
  fullname: Schneider, Christopher
  organization: Department of Mathematics, Ernst Abbe University of Applied Sciences Jena
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  givenname: Benjamin
  surname: Weißing
  fullname: Weißing, Benjamin
  organization: Department of Mathematical Optimization, Friedrich Schiller University Jena
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Cites_doi 10.1017/CBO9780511804441
10.1007/s10957-005-5494-4
10.1080/02331931003665108
10.1016/S0304-0208(08)72857-3
10.1007/978-1-84800-155-8_7
10.1214/009053604000000067
10.1007/978-3-319-55197-5
10.1007/s10589-015-9760-6
10.1007/s10898-013-0098-2
10.1016/S0140-6736(02)07746-2
10.1007/s00186-016-0554-0
10.1609/aaai.v33i01.33013689
10.1007/s10898-013-0136-0
10.1023/A:1008215702611
10.1007/978-3-642-18351-5
10.1007/s00186-008-0220-2
10.1007/s10898-011-9709-y
10.1007/0-387-23081-5_17
10.1111/j.1467-9868.2005.00503.x
10.1007/BF02592221
10.1007/s00186-007-0194-5
10.1007/BF00939046
10.1287/opre.15.1.147
10.1016/0022-247X(86)90234-9
10.1007/s10898-018-0627-0
10.1016/0022-247X(87)90065-5
10.1080/10556788.2015.1025133
10.1137/0108053
10.1093/bioinformatics/btm312
10.1007/s10957-019-01592-x
10.1515/9781400873173
10.1007/978-3-642-54283-1
10.1007/s10898-018-0666-6
10.1007/s10898-010-9588-7
10.24963/ijcai.2019/330
10.1007/978-0-387-84858-7
10.1007/BF01386389
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References CIT0030
CIT0010
CIT0032
CIT0031
CIT0012
CIT0034
CIT0011
CIT0033
Tuy H. (CIT0044) 1983; 8
CIT0014
Kamenev G.K. (CIT0029) 1992; 32
CIT0036
CIT0013
CIT0035
Thieu T.V. (CIT0043) 1983; 8
CIT0016
CIT0038
CIT0015
CIT0037
CIT0018
CIT0017
CIT0039
Bendsøe M.P. (CIT0002) 2003
CIT0019
CIT0041
CIT0040
CIT0021
CIT0020
CIT0042
CIT0001
CIT0023
CIT0045
Guyon I. (CIT0022) 2005; 17
Zhao Z. (CIT0047) 2010; 1
CIT0003
CIT0025
CIT0024
CIT0046
CIT0005
CIT0027
CIT0004
CIT0026
CIT0048
CIT0007
CIT0006
CIT0028
CIT0009
CIT0008
References_xml – volume: 8
  start-page: 3
  year: 1983
  ident: CIT0044
  publication-title: Acta Math. Vietnam
– ident: CIT0005
  doi: 10.1017/CBO9780511804441
– ident: CIT0040
  doi: 10.1007/s10957-005-5494-4
– ident: CIT0021
– ident: CIT0026
  doi: 10.1080/02331931003665108
– volume: 32
  start-page: 136
  year: 1992
  ident: CIT0029
  publication-title: Zh. Vychisl. Mat. Mat. Fiz.
– ident: CIT0020
  doi: 10.1016/S0304-0208(08)72857-3
– ident: CIT0018
  doi: 10.1007/978-1-84800-155-8_7
– ident: CIT0010
  doi: 10.1214/009053604000000067
– ident: CIT0039
  doi: 10.1007/978-3-319-55197-5
– ident: CIT0008
  doi: 10.1007/s10589-015-9760-6
– ident: CIT0024
  doi: 10.1007/s10898-013-0098-2
– ident: CIT0037
  doi: 10.1016/S0140-6736(02)07746-2
– ident: CIT0034
  doi: 10.1007/s00186-016-0554-0
– ident: CIT0016
  doi: 10.1609/aaai.v33i01.33013689
– ident: CIT0031
– ident: CIT0033
  doi: 10.1007/s10898-013-0136-0
– ident: CIT0003
  doi: 10.1023/A:1008215702611
– ident: CIT0023
– ident: CIT0032
  doi: 10.1007/978-3-642-18351-5
– volume: 8
  start-page: 21
  year: 1983
  ident: CIT0043
  publication-title: Acta Math. Vietnam
– ident: CIT0041
  doi: 10.1007/s00186-008-0220-2
– ident: CIT0011
  doi: 10.1007/s10898-011-9709-y
– ident: CIT0013
  doi: 10.1007/0-387-23081-5_17
– volume: 1
  start-page: 1
  year: 2010
  ident: CIT0047
  publication-title: ASU Feature Sel. Reposit.
– ident: CIT0048
  doi: 10.1111/j.1467-9868.2005.00503.x
– ident: CIT0027
  doi: 10.1007/BF02592221
– ident: CIT0042
  doi: 10.1007/s00186-007-0194-5
– ident: CIT0035
  doi: 10.1007/BF00939046
– ident: CIT0046
  doi: 10.1287/opre.15.1.147
– ident: CIT0001
  doi: 10.1016/0022-247X(86)90234-9
– start-page: 221
  year: 2003
  ident: CIT0002
  publication-title: Topology Optimization: Theory, Methods and Applications
– ident: CIT0007
  doi: 10.1007/s10898-018-0627-0
– ident: CIT0009
  doi: 10.1016/0022-247X(87)90065-5
– ident: CIT0015
  doi: 10.1080/10556788.2015.1025133
– ident: CIT0030
  doi: 10.1137/0108053
– ident: CIT0036
  doi: 10.1093/bioinformatics/btm312
– ident: CIT0004
  doi: 10.1007/s10957-019-01592-x
– ident: CIT0038
  doi: 10.1515/9781400873173
– ident: CIT0028
– ident: CIT0014
  doi: 10.1007/978-3-642-54283-1
– ident: CIT0019
– ident: CIT0045
  doi: 10.1007/s10898-018-0666-6
– ident: CIT0012
  doi: 10.1007/s10898-010-9588-7
– ident: CIT0017
  doi: 10.24963/ijcai.2019/330
– volume: 17
  start-page: 545
  year: 2005
  ident: CIT0022
  publication-title: Advances in Neural Information Processing Systems
– ident: CIT0025
  doi: 10.1007/978-0-387-84858-7
– ident: CIT0006
  doi: 10.1007/BF01386389
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Snippet We present an algorithm for approximately solving bounded convex vector optimization problems. The algorithm provides both an outer and an inner polyhedral...
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SubjectTerms 90-08
Algorithms
Apexes
Approximation
convex programming
Mathematical analysis
multiple objective optimization
Optimization
polyhedral approximation
Vector optimization
Title A Benson-type algorithm for bounded convex vector optimization problems with vertex selection
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