Theory of algorithms based on disccroentevexity and its applications

2012 Fiscal Year Final Research Report

• Project/Area Number: 22700007
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Fundamental theory of informatics
• Research Institution: The University of Tokyo
• Principal Investigator: NAGANO Kiyohito 東京大学, 生産技術研究所, 特任助教 (20515176)
• Project Period (FY): 2010 – 2012
• Keywords: 数理計画 / 離散凸解析 / 機械学習

Research Abstract

A submodular function is a natural discrete analogue of a convex function. A number of discrete and continuous optimization problems in various fields, including operations research and machine learning, can be reduced to submodular optimization problems. In our research, we showed some structure properties and gave efficientalgorithms for several submodular optimization problems.

Research Products

• [Journal Article] Equivalence of convex minimization problems over base polytopes (2012)
  • Author(s): Kiyohito Nagano and Kazuyuki Aihara,
  • Journal Title: Japan Journal of Industrial and Applied Mathematics Volume: 29 Pages: 519-534
  • DOI: DOI:10.1007/s13160-012-0083-z
  • Peer Reviewed
• [Journal Article] 基礎技術としての劣モジュラ最適化 (2011)
  • Author(s): 永野清仁
  • Journal Title: オペレーションズ・リサーチ Volume: 56 Pages: 27-32.
• [Journal Article] Submodular fractional programming for balanced clustering (2011)
  • Author(s): Yoshinobu Kawahara, Kiyohito Nagano,and Yoshio Okamoto
  • Journal Title: Pattern Recognition Letters Volume: 32 Pages: 235-243
  • DOI: DOI:10.1016/j.patrec.2010.08.008
  • Peer Reviewed
• [Presentation] Size-constrained submodular minimization through minimum norm base (2012)
  • Author(s): Kiyohito Nagano, Yoshinobu Kawahara,Kazuyuki Aihara
  • Organizer: 21st International Symposium on Mathematical Programming (ISMP 2012)
  • Place of Presentation: ドイツベルリンベルリン工科大学.
  • Year and Date: 2012-08-23
• [Presentation] Exact Approaches to Constrained Submodular Minimization Problems, (2012)
  • Author(s): Kiyohito Nagano
  • Organizer: Modern Aspects of Submodularity,"招待講
  • Place of Presentation: アメリカ合衆国 ジョージア州 アトランタ ジョージア工科大学.
  • Year and Date: 2012-03-21
• [Presentation] Submodular optimization in clustering problems (2011)
  • Author(s): Kiyohito Nagano
  • Organizer: 19th Triennial Conference of the International Federation of Operational Research Societies (IFORS2011)
  • Place of Presentation: オーストラリアメルボルン.
  • Year and Date: 2011-07-11
• [Presentation] Size-constrained submodular minimization through minimum norm base (2011)
  • Author(s): Kiyohito Nagano, Yoshinobu Kawahara, Kazuyuki Aihara
  • Organizer: 28th International Conference on Machine Learning (ICML 2011)
  • Place of Presentation: アメリカ合衆国ワシントン州 ベルビュー.
  • Year and Date: 2011-06-30
• [Presentation] Minimum Average Cost Clustering (2010)
  • Author(s): Kiyohito Nagano, Yoshinobu Kawahara,Satoru Iwata
  • Organizer: 24th Annual Conference on Neural Information Processing Systems (NIPS2010)
  • Place of Presentation: カナダブリティッシュコロンビア州 バンクーバー.
  • Year and Date: 2010-12-07
• [Presentation] Submodular Optimization Based on Combinatorial Convex Structures (2010)
  • Author(s): Kiyohito Nagano
  • Organizer: SIAM Conference on Discrete Mathematics
  • Place of Presentation: アメリカ合衆国テキサス州 オースティン.
  • Year and Date: 2010-06-17
• [Remarks]
  • URL: http://www.sat.t.u-tokyo.ac.jp/~nagano/