Development of Fast Solution Methods based on Sequential Partial Optimization for Large Scale Convex Programming Problems

2011 Fiscal Year Final Research Report

• Project/Area Number: 21560068
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Engineering fundamentals
• Research Institution: Kyushu University
• Principal Investigator: TAKAHASHI Norikazu 九州大学, 大学院・システム情報科学研究院, 准教授 (60284551)
• Project Period (FY): 2009 – 2011
• Keywords: 凸計画問題 / 逐次部分最適化 / 非負行列因子分解 / ニューラルネットワーク / 最大流問題 / 複雑ネットワーク / クラスター係数 / マルチエージェントネットワーク

Research Abstract

We developed sequential partial optimization algorithms for fundamental continuous convex programming problems such as linear programs and convex quadratic programs, and evaluated their characteristics and efficiency through global convergence analysis and numerical experiments. We also carried out theoretical analysis and development of efficient algorithms for various optimization problems arising in the field of information and communication technology. To be more specific, we studied research issues such as efficient computation methods for nonnegative matrix factorization, optimal design methods for recurrent neural networks, maximizing clustering coefficient of complex networks, and optimization of the topology of multi-agent networks for fast consensus, and obtained many important results.

Research Products

• [Journal Article] Maximum clustering coefficient of graphs with given number of vertices and edges (2011)
  • Author(s): Saki Koizuka, Norikazu Takahashi
  • Journal Title: Nonlinear Theory and Its Applications Volume: Vol.2, No.4 Pages: 443-457
  • DOI: DOI:10.1587/nolta.2.443
  • Peer Reviewed
• [Journal Article] Global asymptotic stability of nonlinear circuits related to maximum flow problems (2011)
  • Author(s): Norikazu Takahashi
  • Journal Title: Nonlinear Theory and Its Applications Volume: Vol.2, No.4 Pages: 432-442
  • DOI: DOI:10.1587/nolta.2.432
  • Peer Reviewed
• [Journal Article] Sufficient conditions for one-dimensional cellular neural networks to perform connected component detection (2010)
  • Author(s): Norikazu Takahashi, Ken Ishitobi, Tetsuo Nishi
  • Journal Title: Real World Applications Volume: Vol.11 Pages: 4202-4213
  • DOI: DOI:10.1016/j.nonrwa.2010.05.007
  • Peer Reviewed
• [Presentation] 星グラフに辺を加えたグラフの代数的連結度最大性について (2012)
  • Author(s): 荻原幸之助,深海竜也,高橋規一
  • Organizer: 電子情報通信学会2012年総合大会
  • Place of Presentation: 岡山大学
  • Year and Date: 2012-03-21
• [Presentation] 非負制約付き凸2次計画問題に対する修正乗法型更新アルゴリズム (2012)
  • Author(s): 片山慈朗,高橋規一
  • Organizer: 電子情報通信学会2012年総合大会
  • Place of Presentation: 岡山大学
  • Year and Date: 2012-03-20
• [Presentation] 2-Switch近傍において最大クラスター係数をもつグラフについて (2012)
  • Author(s): 深海竜也, 高橋規一
  • Organizer: 電子情報通信学会回路とシステム研究会
  • Place of Presentation: 九州大学
  • Year and Date: 2012-01-19
• [Presentation] のための修正乗法型更新アルゴリズムとその大域的収束性～ダイバージェンス最小化の場合～ (2012)
  • Author(s): 日比亮太, 高橋規一, Nonnegative Matrix Factorization
  • Organizer: 電子情報通信学会回路とシステム研究会
  • Place of Presentation: 九州大学
  • Year and Date: 2012-01-19
• [Presentation] based Nonnegative Matrix Factorization and its Global Convergence (2011)
  • Author(s): Ryota Hibi, Norikazu Takahashi, A Modified Multiplicative Update Algorithm for Euclidean Distance
  • Organizer: 18th International Conference on Neural Information Processing
  • Place of Presentation: Shanghai, China
  • Year and Date: 2011-11-14
• [Presentation] ある種の正則グラフの代数的連結度極大性に関する一考察 (2011)
  • Author(s): 荻原幸之助, 高橋規一
  • Organizer: 平成23年度電気関係学会九州支部連合大会
  • Place of Presentation: 佐賀大学
  • Year and Date: 2011-09-27
• [Presentation] ある種のブロックグラフの次数保存クラスター係数極大性 (2011)
  • Author(s): 深海竜也,高橋規一
  • Organizer: 平成23年度電気関係学会九州支部連合大会
  • Place of Presentation: 佐賀大学
  • Year and Date: 2011-09-27
• [Presentation] NMFに対する終了条件付き修正乗法型更新アルゴリズム (2011)
  • Author(s): 日比亮太,高橋規一
  • Organizer: 平成23年度電気関係学会九州支部連合大会
  • Place of Presentation: 佐賀大学
  • Year and Date: 2011-09-26
• [Presentation] of Graphs by Means of 2-Switch Method (2011)
  • Author(s): Tatsuya Fukami, Norikazu Takahashi, Controlling Clustering Coefficient
  • Organizer: 2011 International Symposium on Nonlinear Theory and its Applications
  • Place of Presentation: Kobe, Japan
  • Year and Date: 2011-09-05
• [Presentation] On Topology of Networked Multi-Agent Systems for Fast Consensus (2011)
  • Author(s): Kohnosuke Ogiwara, Norikazu Takahashi
  • Organizer: 2011 International Symposium on Nonlinear Theory and its Applications
  • Place of Presentation: Kobe, Japan
  • Year and Date: 2011-09-05
• [Presentation] のための修正乗法型更新アルゴリズムとその大域的収束性～ユークリッド距離最小化の場合～ (2011)
  • Author(s): 日比亮太,高橋規一, Nonnegative Matrix Factorization
  • Organizer: 電子情報通信学会非線形問題研究会
  • Place of Presentation: 斜里町公民館ゆめホール知床
  • Year and Date: 2011-06-30
• [Presentation] 次数保存2辺張り替えに基づくクラスター係数の制御 (2011)
  • Author(s): 深海竜也,高橋規一
  • Organizer: 電子情報通信学会2011年総合大会
  • Place of Presentation: 東京都市大学
  • Year and Date: 2011-03-14
• [Presentation] グラフラプラシアンの第2固有値を最大にする無向グラフ～平均次数が2以下の場合～ (2011)
  • Author(s): 荻原幸之助,高橋規一
  • Organizer: 電子情報通信学会回路とシステム研究会
  • Place of Presentation: 熊本大学
  • Year and Date: 2011-01-26
• [Presentation] シンプレックス法に基づく逐次部分最適化アルゴリズムの収束性について (2010)
  • Author(s): 日比亮太,高橋規一
  • Organizer: 平成22年度電気関係学会九州支部連合大会
  • Place of Presentation: 九州産業大学
  • Year and Date: 2010-09-26
• [Presentation] (2010)
  • Author(s): Norikazu Takahashi, Global Asymptotic Stability Analysis of Nonlinear Circuits for Solving the Maximum Flow Problem
  • Organizer: 2010 International Symposium on Nonlinear Theory and its Applications
  • Place of Presentation: Krakow, Poland
  • Year and Date: 2010-09-07
• [Presentation] 区分線形リカレントニューラルネットワークによる2値ベクトル系列の生成 (2010)
  • Author(s): 高橋規一
  • Organizer: 平成22年度電気学会電子・情報・システム部門大会
  • Place of Presentation: 熊本大学
  • Year and Date: 2010-09-02
• [Presentation] クラスター係数の最大値および極大値に関する考察 (2010)
  • Author(s): 肥塚紗希,高橋規一
  • Organizer: 電子情報通信学会非線形問題研究会
  • Place of Presentation: 鳴門教育大学
  • Year and Date: 2010-08-02
• [Presentation] Analysis of Signal Propagation in 1-D CNNs with the Antisymmetric Template (2010)
  • Author(s): Norikazu Takahashi, Tetsuo Nishi and Hajime Hara
  • Organizer: 12th IEEE International Workshop on Cellular Nanoscale Networks and their Applications
  • Place of Presentation: Berkeley, USA
  • Year and Date: 2010-01-05
• [Presentation] 凸2次計画問題に対する2段階逐次部分最適化アルゴリズムの実験的評価 (2009)
  • Author(s): 小林裕太,高橋規一
  • Organizer: 電子情報通信学会非線形問題研究会
  • Place of Presentation: 屋久島環境文化村センター
  • Year and Date: 2009-11-11
• [Presentation] (2009)
  • Author(s): Yuta Kobayashi, Norikazu Takahashi, A Two-Phase Decomposition Algorithm for Solving Convex Quadratic Programming Problems
  • Organizer: 2009 International Symposium on Nonlinear Theory and its Applications
  • Place of Presentation: Sapporo, Japan
  • Year and Date: 2009-10-21
• [Presentation] On Clustering Coefficients of Graphs with the Fixed Numbers of Vertices and Edges (2009)
  • Author(s): Norikazu Takahashi
  • Organizer: European Conference on Circuit Theory and Design 2009
  • Place of Presentation: Antalya, Turkey
  • Year and Date: 2009-08-27
• [Remarks]
  • URL: http://www-kairo.csce.kyushu-u.ac.jp/~norikazu/homepage.ja.html