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2007 Fiscal Year Final Research Report Summary

Development of numerically stable primal-dual interior point algorithms for solving nonlinear semidefinite programming problems

Research Project

Project/Area Number 18560052
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Engineering fundamentals
Research InstitutionUniversity of Tsukuba

Principal Investigator

YOSHISE Akiko  University of Tsukuba, Graduate School of Systems and Information Engineering, Professor (50234472)

Co-Investigator(Kenkyū-buntansha) FUJISAWA Katsuki  University of Tsukuba, Graduate School of Systems and Information Engineering, Associate Professor (40303854)
YAMAMOTO Yoshitsugu  University of Tsukuba, Graduate School of Systems and Information Engineering, Professor (00119033)
KUNO Takahito  University of Tsukuba, Graduate School of Systems and Information Engineering, Associate Professor (00205113)
SHIGENO Maiko  University of Tsukuba, Graduate School of Systems and Information Engineering, Associate Professor (40272687)
MURAMATSU Masakazu  University of Tsukuba, Graduate School of Systems and Information Engineering, Associate Professor (70266071)
Project Period (FY) 2006 – 2007
KeywordsOptimization / Semidefinite programming / Interior point method / Homogeneous algorithm / Complementarity problem / Nonlinear optimization
Research Abstract

The aim of this research is to develop numerically stable primal-dual interior point methods foe solving nonlinear semidefinite programming problems. The semidefinite programming problem is an optimization problem over a closed convex cone that is not polyhedral unlike the linear programming problem. By this reason, we often observe a problem which has an asymptotic optimal solution but no optimal solution, I.e., any sequence on which the object value converges to the optimal value diverges. This brings us a numerical difficulty in determining the optimality when we apply interior point algorithms to solve the problem. A high accuracy of an optimal solution of the problem is critical if we adopt the problem as an approximation model of a combinatorial optimization problem or a robust optimization problem. To overcome the difficulty, many techniques have been proposed for obtaining a numerical stability of the algorithms. Such techniques are more highly expected when we solve nonlinear semidefinite programming problems. In order to provide one of such techniques, we introduced a homogeneous model for the nonlinear semidefinite programming problem, and showed that for the homogeneous model, (a) a bounded path having a trivial starting point exists, (b) any accumulation point of the path is a solution of the homogeneous model, c if the original problem is solvable then it gives us a finite solution, (d) if the original problem is strongly infeasible, then it gives us a finite certificate proving infeasibility, and (e) a class of algorithms for numerically tracing the path in (a) solves the problem in a polynomial number of iterations under a moderate assumption

  • Research Products

    (34 results)

All 2008 2007 2006 Other

All Journal Article (24 results) (of which Peer Reviewed: 10 results) Presentation (8 results) Remarks (2 results)

  • [Journal Article] Homogencous Algorithms for Monotone Complementarity Problems over Symmetric Cones2008

    • Author(s)
      A.Yoshise
    • Journal Title

      Discussion Paper Series, Institute of Policy and Planning Sciences, University of Tsukuba 1197(CD-ROM)

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] A Simplicial Branch-and-bound Algorithm Conscious of Special Structures in Concave Minimization Problems2008

    • Author(s)
      H. Nagai and T.Kuno
    • Journal Title

      Computational Optimization and Application 39

      Pages: 219-238

    • Description
      「研究成果報告書概要(和文)」より
    • Peer Reviewed
  • [Journal Article] Homogeneous Algorithms for Monotone Complementarity Problems over Symmetric Cones2008

    • Author(s)
      A. Yoshise
    • Journal Title

      Discussion Paper Series, Institute of Policy and Planning Sciences

      Pages: 1197

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] A Simplicial Branch-and-bound Algorithm Conscious of Special Structures in Concave Minimization Problems2008

    • Author(s)
      H. Nagai and T. Kuno
    • Journal Title

      Computational Optimization and Application 39

      Pages: 219-238

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Interies Point Trajectories and a Homogeneous Model for Nonlinear Complementarity Problems over Symmetric Cones2007

    • Author(s)
      A.Yoshise
    • Journal Title

      SIAM Jaon1al on Optimization 17

      Pages: 1129-1153

    • Description
      「研究成果報告書概要(和文)」より
    • Peer Reviewed
  • [Journal Article] Thc Home-Away Assignment Problems and Break Minimization/Maximization Problems in Sports Scheduling2007

    • Author(s)
      A .Suzttka, R. Miyashi!e, A Yoshise and T.Matsui
    • Journal Title

      Pacific Journal of Optimization 3

      Pages: 113-133

    • Description
      「研究成果報告書概要(和文)」より
    • Peer Reviewed
  • [Journal Article] SDPA Project :Solving Large-scale Semidefinite Programs2007

    • Author(s)
      K. Fujisawa, K.Nakata, M. Yarnashita and M. Fukuda
    • Journal Title

      Journal of the Operations Research Society of Japan 50

      Pages: 278-298

    • Description
      「研究成果報告書概要(和文)」より
    • Peer Reviewed
  • [Journal Article] Outer Approximation Method for the Minimum Maximal Flow Problem2007

    • Author(s)
      D.Zen:ke and Y.Yamamoto
    • Journal Title

      Journal of the Operations Research Society of Japan 50

      Pages: 14-30

    • Description
      「研究成果報告書概要(和文)」より
    • Peer Reviewed
  • [Journal Article] A PolynoMial-space Finite Algorithm for Solving a Class Of Reverse Convex Programs2007

    • Author(s)
      T. Kuno and Y.Siguro
    • Journal Title

      筑波大学システム情報工学研究科 コンビュータサイエンス専攻 テクニカルレポート CS-TR07-89

      Pages: 1-10

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Newsvendor Solutions via Conditional Value-at-lisk Minmization2007

    • Author(s)
      J. Gotoh and Y. Takano
    • Journal Title

      EuroPean Journal of Operatio.nal Reseatch 179

      Pages: 80-96

    • Description
      「研究成果報告書概要(和文)」より
    • Peer Reviewed
  • [Journal Article] Towards a Pivoting Pfocedure for a CIass of Second-order Cone Programming Problems Having Multiple Cone Constraints2007

    • Author(s)
      M. Muramatsu
    • Journal Title

      Pacific Joumal of Optimization 3

      Pages: 87-98

    • Description
      「研究成果報告書概要(和文)」より
    • Peer Reviewed
  • [Journal Article] Interior Point Trajectories and a Homogeneous Model for Nonlinear Complementarity Problems over Symmetric Cones2007

    • Author(s)
      A. Yoshise
    • Journal Title

      SIAM Journal on Optimization 17

      Pages: 1129-1153

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] The Home-Away Assignment Problems and Break Minimization/ Maximization Problems in Sports Scheduling2007

    • Author(s)
      A. Suzuka, R. Miyashiro, A. Yoshise and T. Matsui
    • Journal Title

      Pacific Journal of Optimization 3

      Pages: 113-133

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] SDPA Project : Solving Large-scale Semidefinite Programs2007

    • Author(s)
      K. Fujisawa, K.Nakata, M. Yamashita and M. Fukuda,
    • Journal Title

      Journal of the Operations Research Society of Japan 50

      Pages: 278-298

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Outer Approximation Method for the Minimum Maximal Flow Problem2007

    • Author(s)
      D. Zenke and Y. Yamamoto
    • Journal Title

      Journal of the Operations Research Society of Japan 50

      Pages: 14-30

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] A Polynomial-space Finite Algorithm for Solving a Class of Reverse Convex Programs2007

    • Author(s)
      T. Kuno and Y.Siguro
    • Journal Title

      Technical Report, 07-89, Department of Computer Science, Graduate School of Systems and Information Engineering

      Pages: 1-10

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Newsvendor Solutions via Conditional Value-at-risk Minimization2007

    • Author(s)
      J. Gotoh and Y. Takano
    • Journal Title

      European Journal of Operational Research 179

      Pages: 80-96

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Towards a Pivoting Procedure for a Class of Second-order Cone Programming Problems Having Multiple Cone Constraints2007

    • Author(s)
      M. Muramatsu
    • Journal Title

      Pacific Journal of Optimization 3

      Pages: 87-98

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Dependent Randomized Rouding to the Home-away Assignmcllt Problem in Sports Scheduling2006

    • Author(s)
      A. Suzuka, R. Miyastiiro; A. Yosliise and T.Matsui
    • Journal Title

      IEICE TTansactions on Fundamentals of Eleetforiics E89-A/5

      Pages: 1407-1416

    • Description
      「研究成果報告書概要(和文)」より
    • Peer Reviewed
  • [Journal Article] Dependent Randomized Rounding to the Home-away Assignment Problem in Sports Scheduling2006

    • Author(s)
      A. Suzuka R. Miyashiro, A. Yoshise and T. Matsui
    • Journal Title

      IEICE Transactions on Fundamentals of Electronics E89-A/5

      Pages: 1407-1416

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] α-Conservative Apptoximation for Probabilistically Constrained Convex Programs

    • Author(s)
      Y. Takano and J. Gotoh
    • Journal Title

      Computational Optimization and Applications (印刷確定)

    • Description
      「研究成果報告書概要(和文)」より
    • Peer Reviewed
  • [Journal Article] A Note on Sparse SOS apd SDP Relaxations fer Polynomial Optimization Proble

    • Author(s)
      M. Kojima and M. Muramatsu
    • Journal Title

      Computational Optimization and Applications (印刷確定)

    • Description
      「研究成果報告書概要(和文)」より
    • Peer Reviewed
  • [Journal Article] a -Conservative Approximation for Probabilistically Constrained Convex Programs

    • Author(s)
      Y. Takano and J. Gotoh
    • Journal Title

      Computational Optimization and Applications

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] A Note on Sparse SOS and SDP Relaxations for Polynomial Optimization Problems over Symmetric Cones

    • Author(s)
      M. Kojima and M. Muramatsu
    • Journal Title

      Computational Optimization and Applications

    • Description
      「研究成果報告書概要(欧文)」より
  • [Presentation] Homogeneous Algorithms for Monotone Complementarity Problems over Symmetric Cones2008

    • Author(s)
      Akiko Yoshise
    • Organizer
      INFORMS OPT08
    • Place of Presentation
      Hyatt Regency Atlanta, USA
    • Year and Date
      2008-03-15
    • Description
      「研究成果報告書概要(欧文)」より
  • [Presentation] A Homogeneous Algorithms for Monotone Complementarity Problems over Symmetric Cones2007

    • Author(s)
      Akiko Yoshise
    • Organizer
      ICOTA7
    • Place of Presentation
      Kobe International Conference Center, Japan
    • Year and Date
      2007-12-12
    • Description
      「研究成果報告書概要(欧文)」より
  • [Presentation] Interior Maps and Homogeneous Models for Complementarity Problems over Symmetric Cones2007

    • Author(s)
      Akiko Yoshise
    • Organizer
      Annual Meeting of Operations Research Society of Japan, Preliminary Lecture by Best Paper Award Winner
    • Place of Presentation
      National Graduate Institute for Policy Studies, Japan
    • Year and Date
      2007-09-28
    • Description
      「研究成果報告書概要(欧文)」より
  • [Presentation] A Homogeneous Algorithms for Monotone Complementarity Problems over Symmetric Cones2007

    • Author(s)
      Akiko Yoshise
    • Organizer
      ICCOPT07-MOPTA07
    • Place of Presentation
      Mcmaster University, Hamilton, Ontario, Canada
    • Year and Date
      2007-08-14
    • Description
      「研究成果報告書概要(欧文)」より
  • [Presentation] nterior Maps and Homogeneous Models for Complementarity Problems2007

    • Author(s)
      Akiko Yoshise
    • Organizer
      RIMS Meeting on the occasion of 60th birthday of Satoru Fujishige, Discrete Structure and Optimization
    • Place of Presentation
      Kyoto University, Japan
    • Year and Date
      2007-07-28
    • Description
      「研究成果報告書概要(欧文)」より
  • [Presentation] A Homogeneous Algorithms for Monotone Complementarity Problems over Symmetric Cones2007

    • Author(s)
      Akiko Yoshise
    • Organizer
      RIMS Meeting
    • Place of Presentation
      Kyoto University, Japan
    • Year and Date
      2007-07-18
    • Description
      「研究成果報告書概要(欧文)」より
  • [Presentation] A Homogeneous Algorithms for Monotone Complementarity Problems over Symmetric Cones2007

    • Author(s)
      Akiko Yoshise
    • Organizer
      Workshop on Advances in Optimization
    • Place of Presentation
      Tokyo Institute of Technology, Japan
    • Year and Date
      2007-04-20
    • Description
      「研究成果報告書概要(欧文)」より
  • [Presentation] A Homogeneous Algorithms for Monotone Complementarity Problems over Symmetric Cones2007

    • Author(s)
      Akiko Yoshise
    • Organizer
      SM Meeting, Optimization : Modeling and Algorithms
    • Place of Presentation
      Institute of Statistics and Mathematics, Japan
    • Year and Date
      2007-03-22
    • Description
      「研究成果報告書概要(欧文)」より
  • [Remarks] 「研究成果報告書概要(和文)」より

    • URL

      http://infoshako.sk.tsukuba.ac.jp/~yoshise/

  • [Remarks] 「研究成果報告書概要(和文)」より

    • URL

      http://www.trios.tsukuba.ac.jp/Profiles/0004/0000550/profiles.html

URL: 

Published: 2010-02-04  

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