Developments ofcomputational theory of real algebraic geometry for optimization problem

• Project/Area Number: 21340025
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Kyushu University
• Principal Investigator: ANAI Hirokazu 九州大学, マス・フォア・インダストリ研究所, 教授 (20417520)
• Co-Investigator(Kenkyū-buntansha): YOKOYAMA Kazuhiro 立教大学, 理学部, 教授 (30333454)
• Co-Investigator(Renkei-kenkyūsha): YANAMI Hitoshi 富士通研究所, ソフトウェア技術研究所, 研究員 (70417533) ; IWANE Hidenao 富士通研究所, ソフトウェア技術研究所, 研究員 (00470360)
• Project Period (FY): 2009 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥17,160,000 (Direct Cost: ¥13,200,000、Indirect Cost: ¥3,960,000); Fiscal Year 2012: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000); Fiscal Year 2011: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000); Fiscal Year 2010: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000); Fiscal Year 2009: ¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
• Keywords: 数式処理 / 最適化 / 数値 / 数式融合計算 / 記号・代数計算 / パラメトリック最適化 / 記号的最適化手法 / 実代数幾何 / 限量記号消去 / グレブナ基底 / 限量子消去

Research Abstract

In this project we have developed effective and efficient quantifier elimination algorithms for optimization problems. We had many original results on quantifier elimination algorithms and published them in international academic journals. Moreover, we also published textbooks on quantifier elimination and optimization.

Research Products

• [Journal Article] An effective implementation of symbolic-numeric cylindrical algebraic decomposition for quantifier elimination (2013)
  • Author(s): H. Iwane, H. Yanami, H. Anai, K. Yokoyama
  • Journal Title: Theoretical Computer Science Volume: vol. 479 Pages: 43-69
• [Journal Article] An effective implementation of symbolic-numeric cylindrical algebraic decomposition for quantifier elimination (2013)
  • Author(s): H.Iwane, H.Yanami, H.Anai, H.Yokoyama
  • Journal Title: Theoretical Computer Science Volume: 479 Pages: 42-69
  • DOI: 10.1016/j.tcs.2012.10.020
  • Peer Reviewed
• [Journal Article] 自然言語処理と計算代数の接合による数学問題へのアプローチ(<特集>ロボットは東大に入れるか?) (2012)
  • Author(s): 相澤 彰子, 松崎 拓也, 穴井 宏和
  • Journal Title: 人工知能学会誌 Volume: 27(5) Pages: 483-491
  • NAID: 110009496296
  • Peer Reviewed
• [Journal Article] 符号情報利用による数値数式 CAD の効率的な実装,(Computer Algebra : Design of Algorithms, Implementations and Applications (2012)
  • Author(s): 岩根 秀直 , 穴井 宏和, 屋並 仁史
  • Journal Title: 数理解析研究所講究録 Volume: 1815 Pages: 143-151
  • NAID: 120005554194
• [Journal Article] Efficient Arithmetic in Successive Algebraic Extension Fields Using Symmetries (2012)
  • Author(s): S.Orange, G.Renault, K.Yokoyama
  • Journal Title: Mathematics in Computer Science Pages: 217-233
  • Peer Reviewed
• [Journal Article] 数式処理に基づくパラメータ空間法によるロバスト制御系設計 (2011)
  • Author(s): 穴井宏和
  • Journal Title: 電気評論 Volume: 2011 年 3月号 Pages: 15-18
• [Journal Article] Optimizing a Particular Real Root of a Polynomial by a Special Cylindrical Algebraic Decomposition (2011)
  • Author(s): S. Gandy, M. Kanno, H. Anai, K.Yokoyama
  • Journal Title: Mathematics in Computer Science Volume: 5(2) Pages: 209-221
  • Peer Reviewed
• [Journal Article] An SOS-QE Approach to Nonlinear Gain Analysis for Polynomial Dynamical Systems (2011)
  • Author(s): H. Ichihara, H. Anai
  • Journal Title: Mathematics in Computer Science Volume: 5(3) Pages: 303-314
  • Peer Reviewed
• [Journal Article] A Symbolic-Numeric Approach to Multi-Objective Optimization in Manufacturing Design (2011)
  • Author(s): H. Iwane, H. Yanami, H. Anai
  • Journal Title: Mathematics in Computer Science Volume: 5(3) Pages: 315-334
  • Peer Reviewed
• [Journal Article] A Symbolic-Numeric Approach to Multi-Objective Optimization in Manufacturing Design (2011)
  • Author(s): H.Iwane, H.Yanami, H.Anai
  • Journal Title: Mathematics in Computer Science (MCS) Volume: 5-3 Issue: 3 Pages: 315-334
  • DOI: 10.1007/s11786-011-0097-y
  • Peer Reviewed
• [Journal Article] An SOS-QE Approach to Nonlinear Gain Analysis for Polynomial Dynamical Systems (2011)
  • Author(s): H.Ichihara, H.Anai
  • Journal Title: Mathematics in Computer Science (MCS) Volume: 5-3 Issue: 3 Pages: 303-314
  • DOI: 10.1007/s11786-011-0095-0
  • Peer Reviewed
• [Journal Article] Optimizing a Particular Real Root of a Polynomial by a Special Cylindrical Algebraic Decomposition (2011)
  • Author(s): S.Gandy, M.Kanno, H.Anai, K.Yokoyama
  • Journal Title: Mathematics in Computer Science (MCS) Volume: 5-2 Issue: 2 Pages: 209-221
  • DOI: 10.1007/s11786-011-0090-5
  • Peer Reviewed
• [Journal Article] A Note on Distinct Nilpotency Decomposition of Polynomial Ideals over Finite Fields (2010)
  • Author(s): K. Yokoyama
  • Journal Title: Commentarii Mathematici, niversitatis Sancti Pauli Volume: Vol. 59, No.2 Pages: 145-164
  • Peer Reviewed
• [Journal Article] A Note on Distinct Nilpotency Decomposition of Polynomial Ideals over Finite Fields (2010)
  • Author(s): K.Yokoyama
  • Journal Title: Commentarii Mathematici, Universitatis Sancti Pauli Volume: 59・2 Pages: 145-164
  • Peer Reviewed
• [Journal Article] (2010)
  • Author(s): 木村欣司、穴井宏和
  • Journal Title: 「数学セミナー」2010年2月号(日本評論社) Pages: 44-47
• [Journal Article] (2010)
  • Author(s): 木村欣司、穴井宏和
  • Journal Title: 「数学セミナー」2010年3月号(日本評論社) Pages: 52-57
• [Journal Article] Parametric polynomial spectral factorization using the sum of roots and its application to a control design problem (2009)
  • Author(s): H. Anai, S.Hara, M.Kannno, K.Yokoyama
  • Journal Title: J. Symb. Comput Volume: 44(7) Pages: 703-725
  • Peer Reviewed
• [Journal Article] Quintic Polynomials of Hashimoto-Tsunogai, Brumer and Kummer (2009)
  • Author(s): M. Kida, G Renoue, K. Yokoyama
  • Journal Title: International Journal of Number Theory Volume: Vol. 5, No. 4 Pages: 555-571
  • Peer Reviewed
• [Journal Article] Computer Algebra for Guaranteed Accuracy. How Does It Help? (2009)
  • Author(s): M.Kanno, H.Anai
  • Journal Title: Japan J. Indust. Appl. Math Volume: Volume 26, Number 2 Pages: 517-530
  • NAID: 10028169383
  • Peer Reviewed
• [Journal Article] Algebraic Approach to Discrete-time Polynomial Spectral Factorization, Journal of Math-for-Industry (2009)
  • Author(s): M. Kanno, K. Yokoyama, S. Hara, H. Anai
  • Journal Title: Kyushu University Volume: Vol.1 JMI2009A-8 Pages: 57-68
  • Peer Reviewed
• [Journal Article] Parametric polynomial spectral factorization using the sum of roots and its application to a control design problem (2009)
  • Author(s): H.Anai, et al.
  • Journal Title: Journal of Symbolic Computation 44・7 Pages: 703-725
  • Peer Reviewed
• [Journal Article] Algebraic Approach to Discrete-time Polynomial Spectral Factorization (2009)
  • Author(s): M.Kanno, et al.
  • Journal Title: Journal of Math-for-Industry 1・A Pages: 57-68
  • Peer Reviewed
• [Journal Article] Quintic Polynomials of Hashimoto-Tsunogai, Brumer and Kummer (2009)
  • Author(s): M.Kida, et al.
  • Journal Title: International Journal of Number Theory 5・4 Pages: 555-571
  • Peer Reviewed
• [Journal Article] Computation schemes for splitting fields of polynomials (2009)
  • Author(s): S.Orange, et al.
  • Journal Title: Proceedings of the International Symposium on Symbolic and Algebraic Computation 2009 Pages: 279-286
  • Peer Reviewed
• [Journal Article] Solution of algebraic Riccati equations using the sum of roots (2009)
  • Author(s): M.Kanno, et al.
  • Journal Title: Proceedings of the International Symposium on Symbolic and Algebraic Computation 2009 Pages: 215-222
  • Peer Reviewed
• [Journal Article] An Effective Implementation of a Symbolic-Numeric Cylindrical Algebraic Decomposition for Quantifier Elimination (2009)
  • Author(s): H.Iwane, et al.
  • Journal Title: Proceedings of the 3rd International Workshop on Symbolic-Numeric Computation 2009 Pages: 56-64
  • Peer Reviewed
• [Journal Article] Plant/Controller Design Integration for H2 Control by Symbolic-Numeric Hybrid Optimization Based on Sum of Roots Characterization (2009)
  • Author(s): M.Kanno, et al.
  • Journal Title: Proceedings of the 3rd IEEE Multi-conference on Systems and Control 2009 Pages: 1619-1624
  • Peer Reviewed
• [Journal Article] A Symbolic-Numeric Approach to Multi-Parametric Programming for Control Design (2009)
  • Author(s): H.Anai
  • Journal Title: Proceedings of the ICROS-SICE International Joint Conference 2009 Pages: 2535-3520
  • Peer Reviewed
• [Journal Article] A Maple toolbox for parametric robust control system design using symbolic computation (2009)
  • Author(s): H.Noriko, et al.
  • Journal Title: Proceedings of the ICROS-SICE International Joint Conference 2009 Pages: 3520-3524
  • Peer Reviewed
• [Journal Article] A Symbolic-Numeric Approach to Some Classes of Parametric Optimization Problems for Manufacturing Design (2009)
  • Author(s): H.Iwane, et al.
  • Journal Title: Proceedings of the 9th Asian Symposium on Computer Mathematics 2009 Pages: 63-66
  • Peer Reviewed
• [Journal Article] A Symbolic Approach to Nonlinear Gain Analysis of a Class of Nonlinear Dynamical Systems (2009)
  • Author(s): H.Ichihara, H.Anai
  • Journal Title: Proceedings of the 3rd International Conference on Mathematical Aspects of Computer and Information Sciences 2009 Pages: 374-377
  • Peer Reviewed
• [Presentation] 代数幾何的アプローチによる多項式システムの解析 (2013)
  • Author(s): 穴井宏和
  • Organizer: 計測自動制御学会 第13回制御部門大会 特別企画「制御と数学が織り成す産業数学の展開」
  • Place of Presentation: アクロス福岡
  • Year and Date: 2013-03-08
• [Presentation] オークションメカニズムの多項式表現と限量記号消去法を用いたメカニズム設計の自動化 (2012)
  • Author(s): 杉町勇和, 岩崎敦, 横尾真, 穴井宏和
  • Organizer: 日本オペレーションズ・リサーチ学会秋季研究発表会
  • Year and Date: 2012-09-13
• [Presentation] Usage of Modular Techniques for Efficient Computation of Ideal Operations (2012)
  • Author(s): K. Yokoyama
  • Organizer: Computer Algebra in Scientific Computing CASC
  • Year and Date: 2012-09-04
• [Presentation] 時間モデルを用いた並列性能予測の誤差を検討する方法 (2012)
  • Author(s): 折居茂夫, 穴井宏和
  • Organizer: 情報処理学会 第133回ハイパフォーマンスコンピューティング研究発表会
  • Place of Presentation: 有馬ビューホテルうらら
  • Year and Date: 2012-03-26
• [Presentation] 論理関数処理を用いた論理式の簡単化 (2012)
  • Author(s): 岩根秀直, 樋口博之, 穴井宏和
  • Organizer: Risa/Asir Conference 2012+第4回六甲博多計算代数会議
  • Place of Presentation: 神戸大学
  • Year and Date: 2012-03-20
• [Presentation] Computational Real Algebraic Geometry and its Engineering Applications (2012)
  • Author(s): 穴井宏和
  • Organizer: 日本学術振興会日本-欧州先端科学セミナーESF-JSPS Frontier Science Conference for Young Researchers "Mathematics for Innovation : Large and Complex Systems"
  • Place of Presentation: 東京(招待講演)
  • Year and Date: 2012-03-01
• [Presentation] An SOS-QE Approach to Nonlinear Gain Analysis (2011)
  • Author(s): H.Ichihara, H.Anai
  • Organizer: 50th IEEE Conference on Decision and Control and European Control Conference
  • Place of Presentation: Orlando, USA
  • Year and Date: 2011-12-12
• [Presentation] 信号処理への代数幾何的アプローチ,電子情報通信学会ソサイエティ大会企画セッション (2011)
  • Author(s): 穴井宏和
  • Organizer: 信号処理工学の多様性と数理的体系化への挑戦
  • Place of Presentation: 北海道大学
  • Year and Date: 2011-09-13
• [Presentation] Distinct Nilpotency Decomposition of Polynomial Ideals over Finite Fields (2011)
  • Author(s): 横山和弘
  • Organizer: 日本数式処理学会大会
  • Place of Presentation: 神戸大学
  • Year and Date: 2011-09-11
• [Presentation] Construction of Explicit Optimal Value Functions by a Symbolic-Numeric Cylindrical Algebraic Decomposition (2011)
  • Author(s): H.Iwane, A.Kira, H.Anai
  • Organizer: Computer Algebra in Scientific Computing
  • Place of Presentation: Kassel, Germany
  • Year and Date: 2011-09-05
• [Presentation] 非線形ダイン解析に対するSOS-QEアプローチ (2011)
  • Author(s): 市原裕之、穴井宏和
  • Organizer: 第11回計測自動制御学会制御部門大会
  • Place of Presentation: 琉球大学
  • Year and Date: 2011-03-17
• [Presentation] Computational Real Algebraic Geometry and its Engineering Applications (2011)
  • Author(s): 穴井宏和
  • Organizer: 日本学術振興会
  • Place of Presentation: 日本-欧州先端科学セミナー ESF-JSPS Frontier Science Conference for Young Researchers "Mathematics for Innovation: Large and Complex Systems"
  • Year and Date: 2011-03-01
• [Presentation] On parametric optimization techniques for solving recursive formulas (2011)
  • Author(s): 吉良知文, 岩根秀直, 穴井宏和
  • Organizer: 「不確実環境下での柔構造最適化モデリング」第7回研究会
  • Year and Date: 2011-01-29
• [Presentation] On parametric optimization techniques for solving recursive formulas (2011)
  • Author(s): 吉良知文、岩根秀直、穴井宏和
  • Organizer: 「不確実環境下での柔構造最適化モデリング」第7回研究会
  • Place of Presentation: 神奈川大学
  • Year and Date: 2011-01-29
• [Presentation] 非線形ゲイン解析に対するSOS-QE アプローチ (2011)
  • Author(s): 市原裕之, 穴井宏和
  • Organizer: 第11回 計測自動制御学会 制御部門大会
  • Year and Date: 2011-01-28
• [Presentation] 代数的簡略化を用いたモデル予測制御の効率的方法 (2011)
  • Author(s): 梅田裕平, 丸山次人, 志村智洋, 穴井宏和
  • Organizer: 第11回 計測自動制御学会 制御部門大会
  • Year and Date: 2011-01-28
• [Presentation] partial CADの改良 (2010)
  • Author(s): 岩根秀直、屋並仁史、穴井宏和
  • Organizer: 京都大学数理解析研究所研究集会CA-ALIAS 2010
  • Place of Presentation: 京都大学
  • Year and Date: 2010-12-03
• [Presentation] A symbolic-numeric approach to nonlinear dynamical system analysis (2010)
  • Author(s): H. Anai
  • Organizer: SIAM / MSRI Workshop on Hybrid Methodologies for Symbolic-Numeric Computation
  • Year and Date: 2010-11-19
• [Presentation] A symbolic-numeric approach to nonlinear dynamical system analysis (2010)
  • Author(s): H.Anai
  • Organizer: SIAM/MSRI Workshop on Hybrid Methodologies for Symbolic-Numeric Computation
  • Place of Presentation: UC Berkeley, USA
  • Year and Date: 2010-11-19
• [Presentation] 産業数学のすすめ・ものづくり強化に向けて (2010)
  • Author(s): 穴井宏和
  • Organizer: Maple Techno Forum 2010
  • Place of Presentation: 東京コンファレンスセンター品川
  • Year and Date: 2010-10-27
• [Presentation] SyNRAC-A Maple Toolbox for Solving Real Algebraic Constraints (2010)
  • Author(s): H.Iwane, H.Yanami, H.Anai
  • Organizer: The Third International Congress on Mathematical Software (ICMS2010)
  • Place of Presentation: 神戸大学
  • Year and Date: 2010-09-16
• [Presentation] Computer Algebra - what does it bring to control system design? (2010)
  • Author(s): H. Anai
  • Organizer: SICE Annual Conference 2010
  • Year and Date: 2010-08-19
• [Presentation] Computer Algebra-what does it bring to control system design? (2010)
  • Author(s): H.Anai
  • Organizer: SICE Annual Conference 2010
  • Place of Presentation: 台北、台湾
  • Year and Date: 2010-08-19
• [Presentation] Parallel Computation of Determinants of Matrices with Polynomial Entries for robust control design Parallel Symbolic Computation (2010)
  • Author(s): K.Kimura, H.Anai
  • Organizer: Parallel Symbolic Computation 2010
  • Place of Presentation: Grenoble, France
  • Year and Date: 2010-07-21
• [Presentation] CAD における i-projection operator 導入による QE の効率化 (2010)
  • Author(s): 岩根秀直, 穴井宏和, 屋並仁史
  • Organizer: 日本数式処理学会大会
  • Year and Date: 2010-06-12
• [Presentation] CADにおけるi-projection operator導入によるQEの効率化 (2010)
  • Author(s): 岩根秀直、穴井宏和、屋並仁史
  • Organizer: 日本数式処理学会大会
  • Place of Presentation: 名古屋大学
  • Year and Date: 2010-06-12
• [Presentation] A Symbolic-Numeric Approach to Multi-Parametric Programming for Control Design: ICROS-SIC (2009)
  • Author(s): H. Anai
  • Organizer: International Joint Conference 2009
  • Year and Date: 2009-08-20
• [Presentation] A Maple toolbox for parametric robust control system design using symbolic computation (2009)
  • Author(s): H. Noriko, H. Anai, S. Hara
  • Organizer: ICROS-SICE international Joint Conference 2009
  • Year and Date: 2009-08-20
• [Presentation] A Symbolic-Numeric Approach to Multi-Parametric Programming for Control Design: ICROS-SICE (2009)
  • Author(s): H. Anai
  • Organizer: International Joint Conference 2009
  • Year and Date: 2009-08-20
• [Presentation] An Effective Implementation of Symbolic-Nuneric Cylindrical Algebraic Decomposition for Quantifier Elimination (2009)
  • Author(s): H. Iwane, H. Yanami, H. Anai, K. Yokoyama
  • Organizer: 3rd International Workshop on Symbolic-Numeric Computation (SNC)
  • Year and Date: 2009-08-04
• [Presentation] An Effective Implementation of Symbolic-Nuneric Cylindrical Algebraic Decomposition for Quantifier Elimination (2009)
  • Author(s): H. Iwane, H. Yanami, H. Anai, K. Yokoyama
  • Organizer: 3rd International Workshop on Symbolic-Numeric Computation (SNC) 2009
  • Year and Date: 2009-08-04
• [Presentation] Plant/Controller Design Integration for H2 Control by Symbolic-Numeric Hybrid Optimization Based on Sum of Roots Characterization (2009)
  • Author(s): M. Kanno, S. Hara, H. Anai
  • Organizer: 3rd IEEE Multi-conference on Systems and Control (MSC2009)
  • Year and Date: 2009-07-09
• [Presentation] Solution of Algebraic Riccati Equations Using the Sum of Roots (2009)
  • Author(s): M. Kanno, K. Yokoyama, H. Anai, S. Hara
  • Organizer: International Symposium on Symbolic and Algebraic Computation (ISSAC) 2009
  • Year and Date: 2009-07-09
• [Presentation] Computation of the splitting field of a polynomial using its Galois group (2009)
  • Author(s): K.Yokoyama
  • Organizer: International Conference on Mathematics Mechanization
  • Place of Presentation: Academy of Mathematics and Systems Science, 北京
  • Year and Date: 2009-05-12
• [Presentation] Computational Real Algebraic Geometry in Practice
  • Author(s): Hirokazu Anai
  • Organizer: 23rd International Conference on Rewriting Techniques and Applications (RTA'12)
  • Place of Presentation: 名古屋大学
  • Invited
• [Presentation] Usage of Modular Techniques for Efficient Computation of Ideal Operations
  • Author(s): Kazuhiro Yokoyama
  • Organizer: Computer Algebra in Scientific Computing CASC 2012
  • Place of Presentation: Maribor (Slovenia)
  • Invited
• [Presentation] Quantifier Elimination for Solving Real Engineering Problems
  • Author(s): Kazuhiro Yokoyama
  • Organizer: International Symposium on Symbolic Computation in Software Science
  • Place of Presentation: Tunis(Tunisia)
  • Invited
• [Presentation] Sign Definite Condition 専用 Quantifier Elimination の実装高速化のための論理式の簡単化
  • Author(s): 岩根秀直、樋口博之、穴井宏和
  • Organizer: 第２１回日本数式処理学会大会
  • Place of Presentation: 山口大学
• [Book] 数理最適化の実践ガイド (2013)
  • Author(s): 穴井宏和
  • Total Pages: 160
  • Publisher: 講談社
• [Book] 数理最適化の実践ガイド (2013)
  • Author(s): 穴井宏和
  • Total Pages: 158
  • Publisher: 講談社サイエンティフィック
• [Book] QEの計算アルゴリズムとその応用-数式処理による最適化 (2011)
  • Author(s): 穴井宏和、横山和弘
  • Total Pages: 264
  • Publisher: 東京大学出版会
• [Book] QEの計算アルゴリズムとその応用-数式処理による最適化 (2011)
  • Author(s): 穴井宏和・横山和弘
  • Total Pages: 264
  • Publisher: 東京大学出版会
• [Remarks] SyNRAC ダウンロードページ
  • URL: http://jp.fujitsu.com/group/labs/techinfo/freeware/synrac/
• [Remarks] 図書関連ホームページ
  • URL: http://www.utp.or.jp/bd/978-4-13-061406-1.html
• [Remarks]
  • URL: http://www.kspub.co.jp/book/detail/1565104.html
• [Remarks] 数理最適化の実践ガイド | 書籍情報 | 株式会社 講談社サイエンティフィク
  • URL: http://www.kspub.co.jp/book/detail/1565104.html
• [Remarks]
  • URL: http://www.utp.or.jp/bd/978-4-13-061406-1.html