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On Algorithms and Applications of Semidefinite Programming to Combinatorial Optimization

Research Project

Project/Area Number 13640114
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionKYOTO UNIVERSITY

Principal Investigator

TAMURA Akihisa  Research Institute for Mathematical Sciences, Associate Professor, 数理解析研究所, 助教授 (50217189)

Co-Investigator(Kenkyū-buntansha) FURIHATA Daisuke  Osaka University, Cybermedia Center (2001), Lecturer, サイバーメディアセンター(13年度のみ), 講師 (80242014)
FUJIE Tetsuya  Kobe University of Commerce, Institute of Economic Research, Research Associate, 商経学部, 助手 (40305678)
MUROTA Kazuo  Research Institute for Mathematical Sciences, (2001), The University of Tokyo, Graduate School of Information Science and Technology (2002), Full Professor, 数理解析研究所, 教授 (50134466)
OOURA Takuya  Research Institute for Mathematical Sciences, (2002), Research Associate, 数理解析研究所(14年度のみ), 助手 (50324710)
Project Period (FY) 2001 – 2002
Project Status Completed (Fiscal Year 2002)
Budget Amount *help
¥2,400,000 (Direct Cost: ¥2,400,000)
Fiscal Year 2002: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 2001: ¥1,000,000 (Direct Cost: ¥1,000,000)
KeywordsSemidefinite Programming / Discrete Convex Analysis / Algorithms / Bidirected Graphs / Perfect Graphs
Research Abstract

We obtained several results on semidefinite programming and discrete convex analysis and presented these results at international conferences, e.g., International Symposium on Algorithms and Computation, Conference on Integer Programming and Combinatorial Optimization and so on. Here we explain seven results among these.
1) Fujie and Tamura generalized the theory of a convex set relaxation for the maximum weight stable set problem to the generalized stable set problem. They also gave simple proofs for several results for the maximum weight stable set problem.
2) Murota et al. proved that the numerically obtained solution of group symmetric semidefinite program is group symmetric.
3) Murota et al. gave a framework of exploiting the aggregate sparsity pattern over all data matrices of large scale and sparse semidefinite programs.
4) Murota and Tamura gave an efficient algorithm to decide whether a competitive equilibrium exists or not in some economic model by utilizing M-convex submodular flow problem.
5) Tamura devised a new scaling technique and an efficient algorithm for M-convex function minimization problem.
6) Murota and Tamura proved proximity theorems for several discrete convex functions, for example, M2-convex functions, L2-convex functions and so on.
7) Tamura showed a technical result that any L2-convex function can be represented by the convolution of two L-convex functions attaining the infimum in the definition of the convolution. This result gives simple proofs for several known results on L2-convex functions.

Report

(3 results)
  • 2002 Annual Research Report   Final Research Report Summary
  • 2001 Annual Research Report
  • Research Products

    (40 results)

All Other

All Publications (40 results)

  • [Publications] K.Murota, A.Tamura: "Application of M-convex Submodular Flow Problem to Mathematical Economics, in : Eades, P. and Takaoka, T. (eds.) Algorithms and Computation, ISAAC2001"Lecture Notes in Computer Science 2223,Springer. 14-25 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Y.Kanno, M.Ohsaki, K.Murota, N.Katoh: "Group Symmetry in Interior-Point Methods for Semidefinite Program"Optimization and Engineering. 2. 293-320 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T.Fujie, A.Tamura: "On Grotschel-Lovasz-Schrijver's Relaxation of Stable Set Polytopes"Journal of the Operations Research Society of Japan. 45. 285-292 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] A.Tamura: "Coordinatewise Domain Scaling Algorithm for M-Convex Function Minimization, in : Cook, W.J. and Schulz, A.S. (eds.) Integer Programming and Combinatorial Optimization"Lecture Notes in Computer Science 2337,Springer. 21-35 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] S.Moriguchi, K.Murota, A.Shioura: "Scaling Algorithms for M-convex Function Minimization"IEICE Transaction on Fundamentals. E85-A. 922-929 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] R.Ito, T.Fujie, K.Suyama, R.Hirabayashi: "New Design Methods of FIR Filters with Signed Power of Two Coefficients using a New Linear Programming Relaxation with Triangle Inequalties"Proceedings of 2002 IEEE International Symposium on Circuits and Systems. I-813-I-816 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] A.Tamura: "On Convolution of L-Convex Functions"Optimization Methods and Software. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] K.Murota, A.Tamura: "New Characterizations of M-Convex Functions and Their Applications to Economic Equilibrium Models"Discrete Applied Mathematics. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] S.Moriguchi, K.Murota: "Capacity Scaling Algorithm for Scalable M-convex Submodular Flow Problems"Optimization Methods and Software. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] K.Nakata, K.Fujisawa, M.Fukuda, M.Kojima, K.Murota: "Exploiting Sparsity in Semidefinite Programming via Matrix Completion, II : Implementation and Numerical Results"Mathematical Programming. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T.Fujie: "An Exact Algorithm for the Maximum Leaf Spanning Tree Problem"Computers & Operations Research. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] 室田一雄: "離散凸解析"共立出版. 308 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] 田村明久, 村松正和: "最適化法"共立出版. 233 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] 久保幹雄, 田村明久, 松井知己(編集): "応用数理計画ハンドブック"朝倉書店. 1354 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Y. Kanno, M. Ohsaki, K. Murota and N. Katoh: "Group Symmetry in Interior-Point Methods for Semidefinite Program"Optimization and Engineering. 2. 293-320 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T. Fujie and A. Tamura: "On Grotschel-Lovasz-Schrijver's Relaxation of Stable Set Polytopes"Journal of the Operations Research Society of Japan. 45. 285-292 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] S. Moriguchi, K. Murota and A. S. hioura: "Scaling Algorithms for M-convex Function Minimization"IEICE Transaction on Fundamentals. E85-A. 922-929 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] R. Ito, T. Fujie, K. Suyama, R. Hirabayashi: "New Design Methods of FIR Filters with Signed Power of Two Coefficients using a New Linear Programming Relaxation with Triangle Inequalties"Proceedings of 2002 IEEE International Symposium on Circuits and Systems. I-813-I-816 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] A. Tamura: "On Convolution of L-Convex Functions"Optimization Methods and Software. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] K. Murota and A. Tamura: "New Characterizations of M-Convex Functions and Their Applications to Economic Equilibrium Mod-els"Discrete Applied Mathematics. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] S. Moriguchi aud K. Murota: "Capacity Scaling Algorithm for Scalable M-convex Submodular Flow Problems"Optimization Methods and Software. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] K. Nalata, K. Fujisawa, M. Fukuda, M. Kojima and K. Murota: "Exploiting Scarcity in Semidefinite Programming via Matrix Completion, II: Implementation and Numerical Results"Mathematical Programming. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T. Fujie: "An Exact Algorithm for the Maximum Leaf Spanning Thee Problem"Computers & Operations Research. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] K. Murota and A. Tamura, Eades, P. and Takaoka, T. (eds.): "Application of M-convex Submodular Flow Problem to Mathematical Economics, in: Algorithms and Computation, ISAAC2001"Springer, Lecture Notes in Computer Science 2223. 14-25 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] A. Tamura, Cook, W. J. and Schulz, A. S. (eds.): "Coordinatewise Domain Scaling Algorithm for M-Convex Function Minimization, in: Integer Programming and Combinatorial Optimization"Springer, Lecture Notes in Computer Science 2337. 21-35 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T.Fujie, A.Tamura: "On Grotschel-Lovasz-Schrijver's Relaxation of Stable Set Polytopes"Journal of the Operations Research Society of Japan. 45. 285-292 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] A.Tamura: "Coordinatewise Domain Scaling Algorithm for M-Convex Function Minimization"in: Cook, W. J. and Schulz, A. S. (eds.) Integer Programming and Combinatorial Optimization, Lecture Notes in Computer Science, Springer. 2337. 21-35 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] S.Moriguchi, K.Murota, A.Shioura: "Scaling Algorithms for M-convex Function Minimization"IEICE Transaction on Fundamentals. E85-A. 922-929 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] R.Ito, T.Fujie, K.Suyama, R.Hirabayashi: "New Design Methods of FIR Filters with Signed Power of Two Coefficients using a New Linear Programming Relaxation with Triangle Inequalties"Proceedins of 2002 IEEE International Symposium on Circuits and Systems. I. 813-816 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] A.Tamura: "On Convolution of L-Convex Functions"Optimization Methods and Software. (掲載予定).

    • Related Report
      2002 Annual Research Report
  • [Publications] K.Murota, A.Tamura: "New Characterizations of M-Convex Functions and Their Applications to Economic Equilibrium Models"Discrete Applied Mathematics. (掲載予定).

    • Related Report
      2002 Annual Research Report
  • [Publications] S.Moriguchi, K.Murota: "Capacity Scaling Algorithm for Scalable M-convex Submodular Flow Problems"Optimization Methods and Software. (掲載予定).

    • Related Report
      2002 Annual Research Report
  • [Publications] K.Nakata, K.Fujisawa, M.Fukuda, M.Kojima, K.Murota: "Exploiting Sparsity in Semidefinite Programming via Matrix Completion, II : Implementation and Numerical Results"Mathematical Programming. (掲載予定).

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Fujie: "An Exact Algorithm for the Maximum Leaf Spanning Tree Problem"Computers & Operations Research. (掲載予定).

    • Related Report
      2002 Annual Research Report
  • [Publications] 久保幹雄, 田村明久, 松井知己(編集): "応用数理計画ハンドブック"朝倉書店. 1354 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 田村明久, 村松正和: "最適化法"共立出版. 233 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] K.Nakata, K.Fujisawa, M.Fukuda, M.Kojima, K.Murota: "Exploiting sparsity in semidefinite programming via matrix completion II, Implementation and numerical results"Mathematical Programming. (発表予定).

    • Related Report
      2001 Annual Research Report
  • [Publications] Y.Kanno, M.Ohsaki, K.Murota, N.Katoh: "Group symmetry in interior-point methods for semidefinite program"Optimization and Engineering. (発表予定).

    • Related Report
      2001 Annual Research Report
  • [Publications] D.Nakamura, A.Tamura: "A revision of Minty's algorithm for finding a maximum weight stable set of a claw-free graph"Journal of the Operations Research Society of Japan. 44. 194-204 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] D.Furihata: "Finite difference schemes for nonlinear wave equation that inherit energy conservation property"J.Comput.Appl.Math.. 134. 35-57 (2001)

    • Related Report
      2001 Annual Research Report

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Published: 2001-04-01   Modified: 2016-04-21  

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