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Self-Regularity : A New Paradigm for Primal-Dual Interior-Point Algorithms

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Title: Self-Regularity : A New Paradigm for Primal-Dual Interior-Point Algorithms
Description: Research on interior-point methods (IPMs) has dominated the field of mathematical programming for the last two decades. Two contrasting approaches in the analysis and implementation of IPMs are the so-called small-update and large-update methods, although, until now, there has been a notorious gap between the theory and practical performance of these two strategies. This book comes close to bridging that gap, presenting a new framework for the theory of primal-dual IPMs based on the notion of the self-regularity of a function. The authors deal with linear optimization, nonlinear complementarity problems, semidefinite optimization, and second-order conic optimization problems. The framework also covers large classes of linear complementarity problems and convex optimization. The algorithm considered can be interpreted as a path-following method or a potential reduction method. Starting from a primal-dual strictly feasible point, the algorithm chooses a search direction defined by some Newton-type system derived from the self-regular proximity. The iterate is then updated, with the iterates staying in a certain neighborhood of the central path until an approximate solution to the problem is found. By extensively exploring some intriguing properties of self-regular functions, the authors establish that the complexity of large-update IPMs can come arbitrarily close to the best known iteration bounds of IPMs. Researchers and postgraduate students in all areas of linear and nonlinear optimization will find this book an important and invaluable aid to their work.
Authors: Jiming Peng, Cornelis Roos, Tamás Terlaky
Resource Type: eBook.
Subjects: Mathematical optimization, Interior-point methods, Programming (Mathematics)
Categories: MATHEMATICS / Applied, MATHEMATICS / Optimization
Database: eBook Collection (EBSCOhost)
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Header DbId: nlebk
DbLabel: eBook Collection (EBSCOhost)
An: 273040
RelevancyScore: 979
AccessLevel: 6
PubType: eBook
PubTypeId: ebook
PreciseRelevancyScore: 978.796813964844
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  Data: Self-Regularity : A New Paradigm for Primal-Dual Interior-Point Algorithms
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  Data: Research on interior-point methods (IPMs) has dominated the field of mathematical programming for the last two decades. Two contrasting approaches in the analysis and implementation of IPMs are the so-called small-update and large-update methods, although, until now, there has been a notorious gap between the theory and practical performance of these two strategies. This book comes close to bridging that gap, presenting a new framework for the theory of primal-dual IPMs based on the notion of the self-regularity of a function. The authors deal with linear optimization, nonlinear complementarity problems, semidefinite optimization, and second-order conic optimization problems. The framework also covers large classes of linear complementarity problems and convex optimization. The algorithm considered can be interpreted as a path-following method or a potential reduction method. Starting from a primal-dual strictly feasible point, the algorithm chooses a search direction defined by some Newton-type system derived from the self-regular proximity. The iterate is then updated, with the iterates staying in a certain neighborhood of the central path until an approximate solution to the problem is found. By extensively exploring some intriguing properties of self-regular functions, the authors establish that the complexity of large-update IPMs can come arbitrarily close to the best known iteration bounds of IPMs. Researchers and postgraduate students in all areas of linear and nonlinear optimization will find this book an important and invaluable aid to their work.
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  Data: <searchLink fieldCode="AR" term="%22Jiming+Peng%22">Jiming Peng</searchLink><br /><searchLink fieldCode="AR" term="%22Cornelis+Roos%22">Cornelis Roos</searchLink><br /><searchLink fieldCode="AR" term="%22Tamás+Terlaky%22">Tamás Terlaky</searchLink>
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  Data: <searchLink fieldCode="DE" term="%22Mathematical+optimization%22">Mathematical optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Interior-point+methods%22">Interior-point methods</searchLink><br /><searchLink fieldCode="DE" term="%22Programming+%28Mathematics%29%22">Programming (Mathematics)</searchLink>
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RecordInfo BibRecord:
  BibEntity:
    Classifications:
      – Code: 519.6
        Scheme: ddc
        Type: prePub
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: Mathematical optimization
        Type: general
      – SubjectFull: Interior-point methods
        Type: general
      – SubjectFull: Programming (Mathematics)
        Type: general
    Titles:
      – TitleFull: Self-Regularity : A New Paradigm for Primal-Dual Interior-Point Algorithms
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Jiming Peng
      – PersonEntity:
          Name:
            NameFull: Cornelis Roos
      – PersonEntity:
          Name:
            NameFull: Tamás Terlaky
      – PersonEntity:
          Name:
            NameFull: Jiming Peng
      – PersonEntity:
          Name:
            NameFull: Cornelis Roos
      – PersonEntity:
          Name:
            NameFull: Tamás Terlaky
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2002
            – D: 04
              M: 02
              Type: profile
              Y: 2014
          Identifiers:
            – Type: isbn-print
              Value: 9780691091938
            – Type: isbn-print
              Value: 9780691091921
            – Type: isbn-electronic
              Value: 9781400825134
          Titles:
            – TitleFull: Self-Regularity : A New Paradigm for Primal-Dual Interior-Point Algorithms
              Type: main
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