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Development of fast algorithms for semi-infinite programs with conic constraints and application to practical problems

Research Project

Project/Area Number 15K15943
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Mathematical informatics
Research InstitutionInstitute of Physical and Chemical Research (2017-2018)
Tokyo University of Science (2015-2016)

Principal Investigator

Okuno Takayuki  国立研究開発法人理化学研究所, 革新知能統合研究センター, 研究員 (70711969)

Research Collaborator Fukushima Masao  
Hayashi Shunsuke  
Yamashita Nobuo  
Tanaka Mirai  
Project Period (FY) 2015-04-01 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords半無限最適化 / 錐最適化 / 非凸最適化 / アルゴリズム / 交換法 / 主双対パス追跡法 / 半正定値錐, 2次錐 / DC最適化 / パス追跡法 / 逐次2次計画法 / LPニュートン法 / 2次錐計画問題 / 非線形半正定値計画問題 / 半無限半正定値計画問題 / 2ステップ超1次収束 / 混合整数DC計画 / 円詰込問題 / DC計画 / 平滑化法 / 混合整数計画 / 連続緩和法 / 非凸 / 半無限計画法 / 2次錐計画問題 / ホットスタート
Outline of Final Research Achievements

In this research project, we studied optimization problems which can be expressed as the problem of minimizing a given real-valued function subject to inequality and equality constraints. Particularly, we focus on a semi-infinite conic program (SICP) which is a special class of optimization problems having infinitely many inequality constraints (semi-infinite constraints) together with conic constraints.
Our main contribution was to propose several algorithms for finding KKT points of SICPs or closely related optimization problems, where a KKT point is a solution satisfying certain technical conditions related to the problems under consideration. We analyzed conditions under which the proposed algorithms output KKT points. Moreover, we actually implemented the proposed algorithms and showed their efficiency via several numerical experiments.

Academic Significance and Societal Importance of the Research Achievements

半無限錐計画問題は, 有限次元インパルス応答フィルター設計などの工学上多くの重要な諸問題から自然なモデル化を通して出現することが多い. したがって半無限錐計画問題を効率的に解く方法論を立脚し、その解を与えることは, そうした諸問題を効率的な解決, もしくはその糸口を与えることになりうる.
これまで錐制約や半無限制約を別々にもった最適化問題の研究は深く行われてきた. 一方, その両方を兼ね揃えた半無限錐計画問題を解くアルゴリズムの設計のためには二つの構造の特徴をうまく活かすことが重要であるものの, そうした研究は少ない. その意味で本研究成果で得られた手法とその理論は意義があると考えられる.

Report

(5 results)
  • 2018 Annual Research Report   Final Research Report ( PDF )
  • 2017 Research-status Report
  • 2016 Research-status Report
  • 2015 Research-status Report
  • Research Products

    (17 results)

All 2019 2018 2017 2016 2015 Other

All Journal Article (3 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 3 results,  Acknowledgement Compliant: 3 results) Presentation (13 results) (of which Int'l Joint Research: 8 results,  Invited: 1 results) Remarks (1 results)

  • [Journal Article] 無限個の錐制約をもつ半無限計画問題とその解法について2017

    • Author(s)
      奥野貴之
    • Journal Title

      応用数理

      Volume: 印刷中

    • NAID

      130006108874

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] An exchange method with refined subproblems for convex semi-infinite programming problems2016

    • Author(s)
      Takayuki Okuno, Shunsuke Hayashi, Nobuo Yamashita, Kensuke Gomoto
    • Journal Title

      Optimization Methods and Software

      Volume: published online Issue: 6 Pages: 1305-1324

    • DOI

      10.1080/10556788.2015.1124432

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Simplex type algorithm for second-order cone programs via semi-infinite programming reformulation2015

    • Author(s)
      Shunsuke Hayashi, Takayuki Okuno, and Yoshihiko Ito
    • Journal Title

      Optimization Methods and Software

      Volume: published online Issue: 6 Pages: 1272-1297

    • DOI

      10.1080/10556788.2015.1121487

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Presentation] Adaptive LP-Newton method for second-order cone optimization problem2019

    • Author(s)
      Mirai Tanaka
    • Organizer
      The 4th ISM-ZIB-IMI MODAL Workshop on Mathematical Optimization and Data Analysis, The Institute of Statistical Mathematics
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] A primal-dual path following method for nonlinear semi-infinite program with semi-definite constraints2018

    • Author(s)
      Takayuki Okuno
    • Organizer
      OR 2018: International Conference on Operations Research
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] A primal-dual path following method for nonlinear semi-infinite SDPs2018

    • Author(s)
      Takayuki Okuno
    • Organizer
      23rd International Symposium on Mathematical Programming (ISMP)
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] A primal-dual path following method for nonlinear semi-infinite SDPs2018

    • Author(s)
      Takayuki Okuno
    • Organizer
      23rd International Symposium on Mathematical Programming
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] 円詰込み問題に対する混合整数 DC 計画法に基づいた手法2018

    • Author(s)
      増田暁
    • Organizer
      日本オペレーションズリサーチ学会2018年春季研究発表会
    • Related Report
      2017 Research-status Report
  • [Presentation] 混合整数 DC 計画問題に対する整数ギャップのない連続緩和法と平滑化法を用い た手法の提案2017

    • Author(s)
      奥野貴之
    • Organizer
      研究集会「最適化:モデリングとアルゴリズム」
    • Place of Presentation
      政策研究大学院大学
    • Year and Date
      2017-03-23
    • Related Report
      2016 Research-status Report
  • [Presentation] A New Approach for Solving Nonlinear Mixed Integer DC Programs Based on a Continuous Relaxation Without Integrality Gap and Smoothing Technique2017

    • Author(s)
      Takayuki Okuno
    • Organizer
      SIAM Conference on Optimization
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] 混合整数非線形計画問題に対する DC 計画法2016

    • Author(s)
      奥野貴之, 池辺淑子, 松尾健太
    • Organizer
      京都大学 数理解析研究所 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
    • Year and Date
      2016-08-25
    • Related Report
      2016 Research-status Report
  • [Presentation] A Continuous DC Programming Approach to Nonlinear Mixed Integer Programs2016

    • Author(s)
      Takayuki Okuno, Yoshiko Ikebe
    • Organizer
      The Fifth International Conference on Continuous Optimization of the Mathematical Optimization Society Program and Abstracts ICCOPT 2016 Tokyo
    • Place of Presentation
      政策研究大学院大学
    • Year and Date
      2016-08-06
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Presentation] A continuous DC programming approach to nonlinear mixed integer programs without integrality gaps2016

    • Author(s)
      Takayuki Okuno, Yoshiko Ikebe
    • Organizer
      XIVth EUROPT 2016 Workshop on ADVANCES IN CONTINUOUS OPTIMIZATION
    • Place of Presentation
      Warsaw University of Technology
    • Year and Date
      2016-07-01
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Presentation] 半正定値錐制約をもつ半無限計画問題に対するパス追跡型アルゴリズム2015

    • Author(s)
      奥野貴之
    • Organizer
      第27 回RAMP シンポジウム
    • Place of Presentation
      静岡大学浜松キャンパス佐鳴会館(静岡県浜松市)
    • Year and Date
      2015-10-15
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] 半無限半正定値計画問題に対する主双対パス追跡法2015

    • Author(s)
      奥野貴之
    • Organizer
      京都大学数理解析研究所研究集会「新時代を担う最適化:モデル化手法と数値計 算」
    • Place of Presentation
      京都大学数理解析研究所(京都府京都市)
    • Year and Date
      2015-08-31
    • Related Report
      2015 Research-status Report
  • [Presentation] Primal-Dual Path Following Method for Solving Linear Semi-In2015

    • Author(s)
      Takayuki Okuno
    • Organizer
      The 22nd International symposium on mathematical programming
    • Place of Presentation
      Pittsburgh (United States of America)
    • Year and Date
      2015-07-12
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Remarks] Takayuki Okuno's web page

    • URL

      https://sites.google.com/view/takaoku-web-page/english-page

    • Related Report
      2018 Annual Research Report

URL: 

Published: 2015-04-16   Modified: 2020-03-30  

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