Implementations of the quasi-Newton method with positive definite matrix completion

• Project/Area Number: 20560056
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Engineering fundamentals
• Research Institution: Kyoto University
• Principal Investigator: YAMASHITA Nobuo 京都大学, 大学院・情報研究科, 准教授 (30293898)
• Project Period (FY): 2008 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000); Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: 数理工学 / 数理最適化 / 数理計画 / 非線形計画 / 準ニュートン法 / 大規模 / 疎性 / 数理計画問題 / 大規模問題 / 正則化ニュートン法 / 正定値化 / 大規模最適化問題 / 正定値行列補完 / 大規模な問題 / 最小2乗問題 / Levenberg-Marqurdt法 / 非線形最適化

Research Abstract

We showed theoretical and numerical properties of the quasi-Newton method with positive definite matrix completion (MCQN) for the unconstrained minimization problem. Taking into account of the properties, we proposed a hybrid method MCQN and implement it for practical use.

Research Products

• [Journal Article] 制約なし最小化問題に対する勾配法，ニュートン型手法の反復回数の見積もり (2013)
  • Author(s): 山下信雄
  • Journal Title: Transactions of the Operations Research Society of Japan Volume: 56
  • NAID: 110009686119
  • Peer Reviewed
• [Journal Article] Global Complexity Bound Analysis of the Levenberg-Marquardt Method for Monsmooth Equations and its Application to the Monlinear Complementarity Problem (2012)
  • Author(s): Kenji Ueda and Nobuo Yamashita
  • Journal Title: Journal of Optimaztion Theory and Application Volume: Vol152 Pages: 450-467
  • Peer Reviewed
• [Journal Article] Global complexlty bound analysis of the Levenberg-Marquardt method for nonsmooth (2012)
  • Author(s): Kenji Ueda, Nobuo Yamashita
  • Journal Title: Journal of Optimization Theory and Applications Volume: 152 Issue: 2 Pages: 450-467
  • DOI: 10.1007/s10957-011-9907-2
  • Peer Reviewed
• [Journal Article] Convergence Analysis of Sparse Quasi-Newton Updates with Positive Definite Matrix Completion for Two -Dimensional Functions (2011)
  • Author(s): Y. -H.Dai and N.Yamashita
  • Journal Title: Numerical Analysis, Control and Opt imization Volume: Vol. 1 Pages: 61-69
  • Peer Reviewed
• [Journal Article] A Derivative Free Trust Region Algorithm for Unconstained Optimization with Controlled Error (2011)
  • Author(s): J. Takaki and N. Yamashita
  • Journal Title: Numerical Analysis, Control and Optimization Volume: Vol. 1 Pages: 117-145
  • Peer Reviewed
• [Journal Article] リプシッツ連続性に基づく勾配法,ニュートン型手法の計算量解析 (2011)
  • Author(s): 山下信雄, 上田健詞
  • Journal Title: 第23回RAMPシンポジウム予稿集 Volume: 23 Pages: 165-179
• [Journal Article] Convergence Analysis of Sparse Quasi-Newton Updates with Positive Definite Matrix Completion for Two-Dimensional Functions (2011)
  • Author(s): Y.-H.Dai, N.Yamashita
  • Journal Title: Numerical Analysis, Control and Optimization Vol.1 Pages: 61-69
• [Journal Article] A Derivative-Free Trust-Region Algorithm for Unconstained Optimization with Controlled Error (2011)
  • Author(s): J.Takaki, N.Yamashita
  • Journal Title: Numerical Analysis, Control and Optimization Vol.1 Pages: 117-145
• [Journal Article] Convergence Analysis of Sparse Quasi-Newton Updates with Positive Definite Matrix Completion for Two-Dimensional Functions (2011)
  • Author(s): Y.-H.Dai, N.Yamashita
  • Journal Title: Numerical Algebra, Control and Optimization Volume: 1 Pages: 61-69
  • Peer Reviewed
• [Journal Article] A Derivative-Free Trust-Region Algorithm for Unconstained Optimization with Controlled Error (2011)
  • Author(s): J.Takaki, N.Yamashita
  • Journal Title: Numerical Algebra, Control and Optimization Volume: 1 Pages: 117-145
  • Peer Reviewed
• [Journal Article] Convergence Properties of the Regularized Newton Method for the Unconstrained Nonconvex Optimization (2010)
  • Author(s): K. Ueda and N. Ya mashita
  • Journal Title: Applied Mathematics & Optimization Volume: Vol. 62 Pages: 27-46
  • Peer Reviewed
• [Journal Article] On a Global Complexity Bound of the Levenberg Marquardt Method (2010)
  • Author(s): K. Ueda and N. Yamashita
  • Journal Title: Journal of Optimization Theory and Applications Volume: Vol.147 Pages: 443-453
  • Peer Reviewed
• [Journal Article] New Local Search Methods for Improving the lagragian Relaxation Based Unit Commitment Solution (2010)
  • Author(s): T.Seki, N. Yamashita K. Kawamoto
  • Journal Title: IEEE transaction on Power System Volume: Vol25 Pages: 272-283
  • Peer Reviewed
• [Journal Article] Convergence Properties of the Regularized Newton Method for the Unconstrained Nonconvex Optimization (2010)
  • Author(s): K.Ueda, N.Yamashita
  • Journal Title: Applied Mathematics & Optimization Vol.62 Pages: 27-46
• [Journal Article] On a Global Complexity Bound of the Levenberg Marquardt Method (2010)
  • Author(s): K.Ueda, N.Yamashita
  • Journal Title: Journal of Optimization Theory and Applications Vol.147 Pages: 443-453
• [Journal Article] 準ニュートン法の研究とその展望(OR研究の最前線) (2010)
  • Author(s): 山下信雄
  • Journal Title: オペレーションズ・リサーチ 55号 Pages: 243-247
• [Journal Article] Convergence Properties of the Regularized Newton Method for the Unconstrained Nonconvex Optimization (2010)
  • Author(s): K.Ueda, N.Yamashita
  • Journal Title: Applied Mathematics & Optimization Volume: 62 Pages: 27-46
• [Journal Article] On a Global Complexity Bound of the Levenberg-Marquardt Method (2010)
  • Author(s): K.Ueda, N.Yamashita
  • Journal Title: Journal of Optimization Theory and Applications Volume: 147 Pages: 443-453
  • Peer Reviewed
• [Journal Article] New Local Search Methods for Improving the Lagrangian-Relaxation-Based Unit Commitment Solution (2010)
  • Author(s): T.Seki, N.Yamashita, K.Kawamoto
  • Journal Title: IEEE transaction on Power System 25 Pages: 272-283
  • Peer Reviewed
• [Journal Article] Convergence Properties of the Regularized Newton Method for the Unconstrained Nonconvex Optimization (2010)
  • Author(s): K.Ueda, N.Yamashita
  • Journal Title: Applied Mathematics and Optimization
  • Peer Reviewed
• [Journal Article] 準ニュートン法の研究とその展望 (2010)
  • Author(s): 山下信雄
  • Journal Title: オペレーションズリサーチ誌 55 Pages: 243-247
  • NAID: 110007610153
• [Journal Article] An implicit programming approach for the road pricing problem with nonadditive route costs (2008)
  • Author(s): R. P. Agdeppa, N. Yamashita, M. Fukushima
  • Journal Title: Journal of Industrial and Management Optimization 4 Pages: 183-197
  • Peer Reviewed
• [Presentation] An Inexact Coordinate Descent Method for the Weighted L1-regularized Convex Optimization Problem (2012)
  • Author(s): Xiaqin Hua and Nobuo Yamashita
  • Organizer: The 5th International Conference on Optimization and Control with Applications
  • Place of Presentation: Beijing, China
• [Presentation] 大規模凸最適化問題に対する勾配法 (2011)
  • Author(s): 山下信雄
  • Organizer: 情報論的学習理論と機械学習研究会
  • Place of Presentation: 奈良大学
  • Year and Date: 2011-11-01
• [Presentation] 大規模凸計画に対する勾配法-統計・機械学習に関連して- (2011)
  • Author(s): 山下信雄
  • Organizer: システム制御情報学会
  • Place of Presentation: 大阪大学
  • Year and Date: 2011-05-18
• [Presentation] リプシッツ連続性に基づく勾配法,ニュートン型手法の計算量解析 (2011)
  • Author(s): 山下信雄 ,上田健詞
  • Organizer: RAMPシンポジウム
  • Place of Presentation: 関西大学
• [Presentation] 大規模凸計画に対する勾配法 (2011)
  • Author(s): 山下信雄
  • Organizer: 情報論的学習理論(ISBIS)ワークショップ
  • Place of Presentation: 奈良女子大学
• [Presentation] 準ニュートン法の研究とその展望 (2010)
  • Author(s): 山下信雄
  • Organizer: 日本オペレーションズリサーチ学会関西支部
  • Place of Presentation: 大阪府立大学
  • Year and Date: 2010-04-03
• [Presentation] ヘッセ行列の疎構造を利用した準ニュートン法について (2010)
  • Author(s): 山下信雄
  • Organizer: 日本オペレーションズリサーチ学会
  • Place of Presentation: 記念講演
• [Presentation] 準ニュートン法の研究とその展望 (2010)
  • Author(s): 山下信雄
  • Organizer: 日本オペレーションズリサーチ学会関西支部総会
  • Place of Presentation: 招待講演
• [Presentation] 大域的収束性が保証された微分を用いない最適化法について (2009)
  • Author(s): 山下信雄
  • Organizer: RAMPシンポジウム
  • Place of Presentation: くにびきメッセ
  • Year and Date: 2009-09-24
• [Presentation] ヘッセ行列の疎構造を利用した準ニュートン法について (2009)
  • Author(s): 山下信雄
  • Organizer: オペレーションズリサーチ学会
  • Place of Presentation: 長崎大学
  • Year and Date: 2009-09-10
• [Presentation] ラグランジュ緩和法による起動停止問題の解を改善するための新しい局所探索法 (2008)
  • Author(s): 山下信雄
  • Organizer: 日本オペレーションズリサーチ学会
  • Place of Presentation: 札幌コンベンションセンター
  • Year and Date: 2008-09-11
• [Book] 数理工学辞典 (2011)
  • Author(s): 太田快人, 他編
  • Total Pages: 597
  • Publisher: 朝倉書店
• [Book] 数理工学のすすて改訂3版 (2011)
  • Author(s): 福嶋雅夫, 他
  • Total Pages: 127
  • Publisher: 現代数学社
• [Book] 数理計画法 (2008)
  • Author(s): 山下信雄, 福島雅夫
  • Total Pages: 18
  • Publisher: コロナ社
• [Remarks]
• [Remarks] LBFGS法とMCQN法のハイブリッド法のMATLABコード
• [Remarks] MLBFGS法
  • URL: http://www-optima.amp.i.kyoto-u.ac.jp/~nobuo/MLBFGS/MLBFGS.html