Development of iterative methods for construction of control model based on the projection method

• Project/Area Number: 25870577
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Foundations of mathematics/Applied mathematics; Computational science
• Research Institution: Akita Prefectural University
• Principal Investigator: Matsushita Shin-ya 秋田県立大学, システム科学技術学部, 准教授 (20435449)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000); Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: 射影法 / 制約可能性問題 / 線形行列不等式

Outline of Final Research Achievements

This research aims to develop efficient iterative methods for solving problems in control theory. Since linear matrix inequalities which play an important role in system and control theory, can be formulated as convex feasibility problems, we studied iterative methods based on the projection method for convex feasibility problems. We investigated theoretical and numerical properties of the accelerated refection projection method, the Douglas-Rachford method and the Haugazeau-like method for the convex feasibility problem.

Research Products

• [Journal Article] On projection reflection method in Hilbert spaces (2015)
  • Author(s): S. Matsushita, Li Xu
  • Journal Title: Journal of Nonlinear and Convex Analysis Volume: Volume 16 Number 11 Pages: 2221-2226
  • Peer Reviewed
• [Journal Article] Accelerated reflection projection algorithm and its application to the LMI problem (2015)
  • Author(s): Shin-ya Matsushita, Li Xu
  • Journal Title: Optimization Volume: 印刷中 Issue: 11 Pages: 2307-2320
  • DOI: 10.1080/02331934.2014.959012
  • Peer Reviewed
• [Journal Article] On convergence of the Douglas-Rachford method in Hilbert Spaces (2015)
  • Author(s): 松下慎也, 徐粒
  • Journal Title: 京都大学数理解析研究所講究録 Volume: 印刷中
• [Journal Article] On ｆinite ｃonvergence of iterative methods for variational inequalities in Hilbert spaces (2014)
  • Author(s): Shin-ya Matsushita, Li Xu
  • Journal Title: Journal of Optimization Theory and Applications Volume: (印刷中) Issue: 3 Pages: 701-715
  • DOI: 10.1007/s10957-013-0460-z
  • Peer Reviewed
• [Presentation] 最良近似問題について (2015)
  • Author(s): 松下慎也
  • Organizer: 2015日本数学会秋季総合分科会
  • Place of Presentation: 京都産業大学
  • Year and Date: 2015-09-15
• [Presentation] On convergence of the methods for best approximation problem (2015)
  • Author(s): 松下慎也
  • Organizer: 非線形解析学と凸解析学の研究
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2015-09-08
• [Presentation] Douglas-Rachford法について (2014)
  • Author(s): 松下慎也
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 広島大学
  • Year and Date: 2014-09-27
• [Presentation] On Convergence of the Douglas-Rachford Method (2014)
  • Author(s): 松下慎也
  • Organizer: 京都大学数理解析研究所研究集会"非線形解析学と凸解析学の研究"
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2014-08-21
• [Presentation] On accelerated projection methods (2013)
  • Author(s): Shin-ya Matsushita, Li Xu
  • Organizer: The eighth international conference on Nonlinear Analysis and Convex Analysis
  • Place of Presentation: 弘前大学
• [Presentation] On projections methods in Hilbert spaces (2013)
  • Author(s): Shin-ya Matsushita, Li Xu
  • Organizer: The International Conference on Non linear Analysis and Optimization
  • Place of Presentation: National Sun Yat-sen University, Taiwan