錐制約付き半無限計画問題のフィルタ設計およびＤＳＭ通信に対する応用

2013 年度 研究成果報告書

• 研究課題/領域番号: 22760064
• 研究種目: 若手研究(B)
• 配分区分: 補助金
• 研究分野: 工学基礎
• 研究機関: 東北大学 (2013); 京都大学 (2010-2012)
• 研究代表者: 林 俊介 東北大学, 情報科学研究科, 准教授 (20444482)
• 研究期間 (年度): 2010-04-01 – 2014-03-31
• キーワード: 数理工学 / 最適化 / 半無限計画 / 錐計画 / フィルタ設計

研究概要

当初，申請書に記述した本研究の目的は，錐制約付き半無限計画問題に対する効率的なアルゴリズムの開発と，そのアルゴリズムの現実問題（フィルタ設計やDSM通信など）への応用ということであった．そのうち，アルゴリズムの開発に関しては，十分な成果が得られた．特に，半無限錐計画問題に対する正則化交換法を提案し，SIAM Journal on Optimizationに採録されたことが最も大きな成果と言えよう．一方，現実問題の応用に関しては，DSM通信に関しては論文として発表できるほどの結果が得られなかったが，フィルタ設計に関しては，正則化交換法をベクトルチェビシェフ問題に適用し良好な結果が得られた．

研究成果

• [雑誌論文] A smoothing method with appropriate parameter control based on Fischer-Burmeister function for second-order cone complementarity problems (2013)
  • 著者名/発表者名: Yasushi Narushima, Hideho Ogasawara, and Shunsuke Hayashi
  • 雑誌名: Abstract and Applied Analysis 巻: 830698 ページ: 1-16
  • 査読あり
• [雑誌論文] A smoothing SQP method for mathematical programs with linear second-order cone complementarity constraints (2013)
  • 著者名/発表者名: Hiroshi Yamamura, Takayuki Okuno, Shunsuke Hayashi, and Masao Fukushima
  • 雑誌名: Pacific Journal of Optimization 巻: 9 ページ: 345-372
  • 査読あり
• [雑誌論文] SDP reformulation for robust optimization problems based on nonconvex QP duality (2013)
  • 著者名/発表者名: Ryoichi Nishimura, Shunsuke Hayashi, and Masao Fukushima
  • 雑誌名: Computational Optimization and Applications 巻: 55 ページ: 21-47
  • 査読あり
• [雑誌論文] A regularized explicit exchange method for semi-infinite programs with an infinite number of conic constraints (2012)
  • 著者名/発表者名: Takayuki Okuno, Shunsuke Hayashi, and Masao Fukushima
  • 雑誌名: SIAM Journal on Optimization 巻: 22 ページ: 1009-1028
  • 査読あり
• [雑誌論文] Semidefinite complementarity reformulation for robust Nash equilibrium problems with Euclidean uncertainty sets (2012)
  • 著者名/発表者名: Ryoichi Nishimura, Shunsuke Hayashi, and Masao Fukushima
  • 雑誌名: Journal of Global Optimization 巻: 53 ページ: 107-120
  • 査読あり
• [雑誌論文] Celis-Dennis-Tapia based approach to quadratic fractional programming problems with two quadratic constraints (2011)
  • 著者名/発表者名: Ailing Zhang and Shunsuke Hayashi
  • 雑誌名: Numerical Algebra, Control and Optimization 巻: 1 ページ: 83-98
  • 査読あり
• [学会発表] Explicit exchange algorithm for convex semi-infinite programming problems with second-order cone constraints (2013)
  • 著者名/発表者名: Shunsuke Hayashi, Liping Zhang, and Soon-Yi Wu
  • 学会等名: The 9th International Conference on Optimization : Techniques and Applications (ICOTA9)
  • 発表場所: Taipei, Taiwan
  • 年月日: 2013-12-14
• [学会発表] Equilibrium problems related to conic complementarity problems (2013)
  • 著者名/発表者名: Shunsuke Hayashi
  • 学会等名: NCTS seminar, National Center for Theoretical Sciences
  • 発表場所: National Cheng Kung University, Tainan, Taiwan
  • 年月日: 2013-09-15
• [学会発表] Sl1QP based algorithm with trust region technique for nonlinear second-order cone programs (2013)
  • 著者名/発表者名: Kohei Yasuda, Takayuki Okuno, and Shunsuke Hayashi
  • 学会等名: The 26th European Conference on Operational Research (EURO2013) / EURO-INFORMS Joint International Meeting
  • 発表場所: Rome, Italy
  • 年月日: 2013-07-07
• [学会発表] A smoothing method with appropriate parameter control based on Fischer-Burmeister function for second-order cone complementarity problems (2013)
  • 著者名/発表者名: Yasushi Narushima, Hideho Ogasawara, and Shunsuke Hayashi
  • 学会等名: The 11th EUROPT Workshop on Advances in Continuous Optimization (EUROPT2013)
  • 発表場所: Florence (Firenze), Italy
  • 年月日: 2013-06-28
• [学会発表] Robust optimization equilibrium and conic complementarity problems (2012)
  • 著者名/発表者名: Shunsuke Hayashi
  • 学会等名: Colloquium of Mathematics Department
  • 発表場所: National Taiwan Normal University, Taipei, Taiwan
  • 年月日: 2012-09-12
• [学会発表] A smoothing SQP method for mathematical programs with second-order cone complementarity constraints (2012)
  • 著者名/発表者名: Hiroshi Yamamura, Takayuki Okuno, Shunsuke Hayashi, and Masao Fukushima
  • 学会等名: The 21st International Symposium on Mathematical Programming (ISMP2012)
  • 発表場所: Berlin, Germany
  • 年月日: 2012-08-12
• [学会発表] The αBB based cutting plane method for semi-infinite program with multi-dimensional index set (2012)
  • 著者名/発表者名: Kensuke Goumoto and Shunsuke Hayashi
  • 学会等名: The 25th European Conference on Operational Research (EURO2012)
  • 発表場所: Vilnius, Lithuania
  • 年月日: 2012-07-10
• [学会発表] A smoothing SQP method for mathematical programs with second-order cone complementarity constraints (2012)
  • 著者名/発表者名: Hiroshi Yamamura, Takayuki Okuno, Shunsuke Hayashi, and Masao Fukushima
  • 学会等名: The 10th EUROPT Workshop on Advances in Continuous Optimization (EUROPT2012)
  • 発表場所: Siauliai, Lithuania
  • 年月日: 2012-07-06
• [学会発表] Robust Wardrop equilibrium in traffic assignment problem with uncertain data (2012)
  • 著者名/発表者名: Yoshihiko Ito and Shunsuke Hayashi
  • 学会等名: Nanjing-Kyoto Joint Workshop on Algorithms, Optimization and Numerical Analysis 2012
  • 発表場所: Kyoto, Japan
  • 年月日: 2012-03-12
• [学会発表] 錐計画と半無限計画におけるアルゴリズムと応用 (2011)
  • 著者名/発表者名: 林 俊介
  • 学会等名: 日本オペレーションズ・リサーチ学会 「数理モデルとその応用」研究部会 第13回研究集会
  • 発表場所: 金沢学院大学大学院サテライト教室
  • 年月日: 2011-10-01
• [学会発表] Semi-infinite program with infinitely many conic constraints : optimality condition and algorithms (2011)
  • 著者名/発表者名: Takayuki Okuno, Shunsuke Hayashi, and Masao Fukushima
  • 学会等名: The 5th Sino-Japan Optimization Meeting (SJOM 2011)
  • 発表場所: Beijing, China
  • 年月日: 2011-09-27
• [学会発表] Robust Wardrop equilibrium in uncertain traffic assignment problem : second-order cone based model (2011)
  • 著者名/発表者名: Yoshihiko Ito and Shunsuke Hayashi
  • 学会等名: NCTS seminar
  • 発表場所: National Center for Theoretical Sciences, National Cheng Kung University, Tainan, Taiwan
  • 年月日: 2011-09-15
• [学会発表] Robust Nash equilibria for games with uncertain data (2011)
  • 著者名/発表者名: Shunsuke Hayashi
  • 学会等名: NCTS seminar
  • 発表場所: National Center for Theoretical Sciences, National Cheng Kung University, Tainan, Taiwan
  • 年月日: 2011-09-13
• [学会発表] ロバストWardrop均衡問題と二次錐相補性問題への変換 (2011)
  • 著者名/発表者名: 伊藤好彦, 高橋 仁, 林 俊介
  • 学会等名: RIMS研究集会「最適化手法の深化と広がり」
  • 発表場所: 京都大学数理解析研究所
  • 年月日: 2011-07-21
• [学会発表] Semi-infinite program with infinitely many conic constraints : optimality conditions and globally convergent algorithm (2011)
  • 著者名/発表者名: Takayuki Okuno, Shunsuke Hayashi, and Masao Fukushima
  • 学会等名: The 19th Triennial Conference of the International Federation of Operational Research Societies (IFORS2011)
  • 発表場所: Melbourne, Australia
  • 年月日: 2011-07-15
• [学会発表] Second-order cone complementarity reformulation for robust Wardrop equilibrium problems in traffic assignment with uncertain data (2011)
  • 著者名/発表者名: Yoshihiko Ito, Hitoshi Takahashi, and Shunsuke Hayashi
  • 学会等名: The 9th EUROPT Workshop on Advances in Continuous Optimization
  • 発表場所: Ballarat, Australia
  • 年月日: 2011-07-08
• [学会発表] Second-order cone based reformulation for robust Wardrop equilibrium problems (2011)
  • 著者名/発表者名: Yoshihiko Ito, Hitoshi Takahashi, and Shunsuke Hayashi
  • 学会等名: SIAM Conference on Optimization (OP11)
  • 発表場所: Darmstadt, Germany
  • 年月日: 2011-05-18
• [学会発表] Convergence analysis of an explicit exchange method for convex semi-infinite programming problems with second-order cone constraints (2010)
  • 著者名/発表者名: Shunsuke Hayashi, Soon-Yi Wu, and Liping Zhang
  • 学会等名: The 8th International Conference on Optimization : Techniques and Applications (ICOTA8)
  • 発表場所: Shanghai, China
  • 年月日: 2010-12-11
• [学会発表] SDP reformulation for robust LPs and SOCPs based on nonconvex QP duality (2010)
  • 著者名/発表者名: Ryoichi Nishimura, Shunsuke Hayashi, and Masao Fukushima
  • 学会等名: NCTS seminar
  • 発表場所: National Center for Theoretical Sciences, National Cheng Kung University, Tainan, Taiwan
  • 年月日: 2010-09-07
• [学会発表] Optimality conditions and regularized explicit exchange method for convex semi-infinite programs with infinitely many conic constraints (2010)
  • 著者名/発表者名: Takayuki Okuno, Shunsuke Hayashi, and Masao Fukushima
  • 学会等名: NCTS seminar, National Center for Theoretical Sciences
  • 発表場所: National Cheng Kung University, Tainan, Taiwan
  • 年月日: 2010-08-31
• [学会発表] Explicit exchange method for convex semi-infinite programming problems with second-order cone constraints (2010)
  • 著者名/発表者名: Shunsuke Hayashi, Soon-Yi Wu, and Liping Zhang
  • 学会等名: NCTS seminar
  • 発表場所: National Center for Theoretical Sciences, National Cheng Kung University, Tainan, Taiwan
  • 年月日: 2010-08-24
• [学会発表] Semidefinite complementarity reformulation for robust Nash equilibrium problems based on the duality of nonconvex quadratic programming (2010)
  • 著者名/発表者名: Ryoichi Nishimura, Shunsuke Hayashi, and Masao Fukushima
  • 学会等名: International Conference on Optimization
  • 発表場所: Simulation and Control, Ulaanbaatar, Mongolia
  • 年月日: 2010-07-26
• [学会発表] Optimality conditions and regularized explicit exchange method for convex semi-infinite programs with infinitely many conic constraints (2010)
  • 著者名/発表者名: Takayuki Okuno, Shunsuke Hayashi, and Masao Fukushima
  • 学会等名: 24th European Conference on Operational Research (EURO XXIV)
  • 発表場所: Lisbon, Portugal
  • 年月日: 2010-07-11
• [学会発表] Robust Nash equilibria in incomplete information games : semidefinite complementarity reformulation and equilibrium behavior (2010)
  • 著者名/発表者名: Ryoichi Nishimura, Shunsuke Hayashi, and Masao Fukushima
  • 学会等名: The 8th EUROPT Workshop on Advances in Continuous Optimization
  • 発表場所: Aveiro, Portugal
  • 年月日: 2010-07-09
• [図書] "半無限計画問題", 太田快人・酒井英明・高橋豊・田中利幸・永持仁・福島雅夫(編集),数理工学事典 (2011)
  • 著者名/発表者名: 林 俊介
  • 総ページ数: 563-566(616)
  • 出版者: 朝倉書店
• [備考]
  • URL: http://www.plan.civil.tohoku.ac.jp/opt/hayashi/