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Conic Programming: Degeneracy and Modeling

Research Project

Project/Area Number 26330025
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Mathematical informatics
Research InstitutionThe University of Electro-Communications

Principal Investigator

Muramatsu Masakazu  電気通信大学, 大学院情報理工学研究科, 教授 (70266071)

Co-Investigator(Kenkyū-buntansha) 土谷 隆  政策研究大学院大学, 政策研究科, 教授 (00188575)
Project Period (FY) 2014-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2014: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Keywords錐線形計画 / 半正定値計画 / 2次錐計画 / モデリング / 多項式計画 / 退化 / Conic linear programming / facial reduction / weak infeasibility / 弱許容性 / 弱非許容性 / 完全正値行列
Outline of Final Research Achievements

It is known that the semidefinite programming (SDP) relaxation method for polynomial optimization problems (POPs) can sometimes find the optimal value of POP although the true optimal value of SDP is different from the value. We gave a theoretical explanation for the mysterious phenomenon. This result is exactly to accomplish (part of) the original research objective. In addition, we gave new theoretical findings on degeneracy such as weak infeasibility in second-order programming problems and SDPs. In particular, we propose a new decomposition method for conic feasibility problems, and succeeded in shrinking the feasibility problem into smaller problems.

Report

(5 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (26 results)

All 2017 2016 2015 2014 Other

All Int'l Joint Research (1 results) Journal Article (5 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 5 results,  Acknowledgement Compliant: 5 results) Presentation (19 results) (of which Int'l Joint Research: 9 results,  Invited: 1 results) Remarks (1 results)

  • [Int'l Joint Research] University of Waterloo(Canada)

    • Related Report
      2015 Research-status Report
  • [Journal Article] Pure Nash Equilibria of Competitive Diffusion Process on Toroidal Grid Graphs2016

    • Author(s)
      Yuki Sukenari, Kunihito Hoki, Satoshi Takahashi, Masakazu Muramatsu
    • Journal Title

      Discrete Applied Mathematics

      Volume: 215 Pages: 31-40

    • DOI

      10.1016/j.dam.2016.07.021

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] 畳み込みニューラルネットワークを用いた囲碁における一局の棋譜からの棋力推定2016

    • Author(s)
      荒木伸夫、保木邦仁、村松正和
    • Journal Title

      情報処理学会論文誌

      Volume: 57 Pages: 2365-2373

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] A Structural Geometrical Analysis of Weakly Infeasible SDPs2016

    • Author(s)
      Bruno F. Lourenco, Masakazu Muramatsu, Takashi Tsuchiya
    • Journal Title

      Journal of Operations Research Society of Japan

      Volume: 59 Pages: 241-257

    • NAID

      130005163067

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Perturbed sums-of-squares theorem for polynomial optimization and its applications2016

    • Author(s)
      Masakazu Muramatsu, Hayato Waki, Levent Tuncel
    • Journal Title

      Optimization Methods and Software

      Volume: 31 Issue: 1 Pages: 134-156

    • DOI

      10.1080/10556788.2015.1052969

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Weak infeasibility in second order cone programming2015

    • Author(s)
      Bruno F. Lourenco , Masakazu Muramatsu, Takashi Tsuchiya
    • Journal Title

      Optimization letters

      Volume: First online Issue: 8 Pages: 1-13

    • DOI

      10.1007/s11590-015-0982-4

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Presentation] Network Congestion Minimization Models Based on Robust Optimization2017

    • Author(s)
      Bimal Chandra Das
    • Organizer
      研究集会「最適化:モデリングとアルゴリズム」
    • Place of Presentation
      統計数理研究所(東京都・立川市)
    • Year and Date
      2017-03-23
    • Related Report
      2016 Research-status Report
  • [Presentation] An extension of Chubanov's algorithm to symmetric cone feasibility problems2017

    • Author(s)
      Bruno F. Lourenco
    • Organizer
      研究集会「最適化:モデリングとアルゴリズム」
    • Place of Presentation
      統計数理研究所(東京都・立川市)
    • Year and Date
      2017-03-23
    • Related Report
      2016 Research-status Report
  • [Presentation] 対称錐に対する Chubanov のアルゴリズムの拡張2017

    • Author(s)
      Bruno F. Lourenco
    • Organizer
      日本オペレーションズ・リサーチ学会2017年春季研究発表会
    • Place of Presentation
      沖縄県市町村自治会館(沖縄県・那覇市)
    • Year and Date
      2017-03-17
    • Related Report
      2016 Research-status Report
  • [Presentation] 三角形総面積最大化問題に関する研究2017

    • Author(s)
      市橋志朗
    • Organizer
      日本オペレーションズ・リサーチ学会2017年春季研究発表会
    • Place of Presentation
      沖縄県市町村自治会館(沖縄県・那覇市)
    • Year and Date
      2017-03-16
    • Related Report
      2016 Research-status Report
  • [Presentation] Application of SOCP in Power Efficient Networks2017

    • Author(s)
      Bimal C. Das, Eiji Oki, and Masakazu Muramatsu
    • Organizer
      SIAM Conference on Optimization 17
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] An Extension of Chubanov's Algorithm to Symmetric Cones2017

    • Author(s)
      Bruno Lourenco, Tomonari Kitahara, Masakazu Muramatsu, Takashi Tsuchiya
    • Organizer
      SIAM Conference on Optimization 17
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Partial Polyhedrality and Facial Reduction2017

    • Author(s)
      Masakazu Muramatsu, Bruno Lourenco, Takashi Tsuchiya,
    • Organizer
      SIAM Conference on Optimization 17
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 内点オラクルによる錐線形計画問題の完全な求解2016

    • Author(s)
      Bruno F. Lourenco
    • Organizer
      日本オペレーションズ・リサーチ学会秋季研究発表会
    • Place of Presentation
      山形大学(山形県・山形市)
    • Year and Date
      2016-09-16
    • Related Report
      2016 Research-status Report
  • [Presentation] Network congestion minimization models based on robust optimization2016

    • Author(s)
      Bimal Chandra Das
    • Organizer
      研究集会「最適化技法の最先端と今後の展開」
    • Place of Presentation
      京都大学数理解析研究所(京都府・京都市)
    • Year and Date
      2016-08-25
    • Related Report
      2016 Research-status Report
  • [Presentation] Analysis on conic programing via facial reduction2016

    • Author(s)
      Masakazu Muramatsu
    • Organizer
      Workshop on Advances in Optimization
    • Place of Presentation
      Tokyo, Japan
    • Year and Date
      2016-08-13
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Presentation] A Mixed-Integer SOCP Model for Robust and Power Efficient Networks2016

    • Author(s)
      Bimal Chandra Das
    • Organizer
      International Conference on Continous Optimization 2016
    • Place of Presentation
      Tokyo, Japan
    • Year and Date
      2016-08-09
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Presentation] Weak Infeasibility, Facial Reduction, and Geometry in Conic Programming2016

    • Author(s)
      Masakazu Muramatsu
    • Organizer
      International Conference on Continous Optimization 2016
    • Place of Presentation
      Tokyo, Japan
    • Year and Date
      2016-08-09
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Presentation] Solving SDP completely with an Interior-Point Oracle2016

    • Author(s)
      Takashi Tsuchiya
    • Organizer
      International Conference on Continous Optimization 2016
    • Place of Presentation
      Tokyo, Japan
    • Year and Date
      2016-08-09
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Presentation] FRA-Poly, Partial Polyhedrality and Facial Reduction2016

    • Author(s)
      Bruno F. Lourenco
    • Organizer
      International Conference on Continous Optimization 2016
    • Place of Presentation
      Tokyo, Japan
    • Year and Date
      2016-08-08
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Presentation] Weak infeasibility, facial reduction, and duality in conic programming2016

    • Author(s)
      Masakazu Muramatsu
    • Organizer
      The 10th International Conference on Optimization: Techniques and applications
    • Place of Presentation
      Ulaanbaatar, Mongolia
    • Year and Date
      2016-07-23
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Presentation] A Relative Interior Seeking Procedure for Second Order Cone Programming and Feasibility Issues2015

    • Author(s)
      Bruno F. Lourenco
    • Organizer
      22nd International Symposium on Mathematical Programming
    • Place of Presentation
      Pittsburgh, USA
    • Year and Date
      2015-07-12
    • Related Report
      2015 Research-status Report
  • [Presentation] Weak Status of Conic Programming2014

    • Author(s)
      Masakazu Muramatsu
    • Organizer
      The First Pacific Optimization Conference
    • Place of Presentation
      Wuxi, China
    • Year and Date
      2014-10-31
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] 完全正値性の判定に関する数値実験2014

    • Author(s)
      田口良典、高橋里司、村松正和
    • Organizer
      数理解析研究所研究集会「最適化アルゴリズムの進展:理論・応用・実装」
    • Place of Presentation
      京都大学
    • Year and Date
      2014-09-24 – 2014-09-25
    • Related Report
      2014 Research-status Report
  • [Presentation] A Geometrical Analysis of Weak Infeasibility in Semidefinite Programming and Related Issues2014

    • Author(s)
      Bruno F. Lourenco, Masakazu Muramatsu, and Takashi Tsuchiya
    • Organizer
      SIAM Conference on Optimization
    • Place of Presentation
      San Diego, USA
    • Year and Date
      2014-05-22
    • Related Report
      2014 Research-status Report
  • [Remarks] 村松研究室

    • URL

      http://www.jsb.cs.uec.ac.jp

    • Related Report
      2016 Research-status Report

URL: 

Published: 2014-04-04   Modified: 2019-03-29  

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