Reconstruction of variational analysis through industrial mathematics

• Project/Area Number: 22740057
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Tokyo University of Marine Science and Technology
• Principal Investigator: SEKIGUCHI Yoshiyuki 東京海洋大学, 海洋科学技術研究科, 准教授 (50434890)
• Project Period (FY): 2010-04-01 – 2014-03-31
• Project Status: Completed (Fiscal Year 2013)
• Budget Amount: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000); Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: 変分解析 / 最適化理論 / 関数解析 / 代数幾何 / 最適化問題 / 凸代数幾何 / 関数解析学 / 解析学 / 数理工学 / アルゴリズム

Research Abstract

We considered quantitative analysis of metric regularity in variational analysis and inequality systems on Banach spaces by functional analytic methods. In addition, we studied theoretical properties of a algorithm for obtaining a global minimum of polynomial optimization problems. Our main results are the following:
1. We gave a formula for modulus of regularity of inequality systems on the space of continuous function. 2. We improved estimates of performance of an SRPT scheduling algorithm by optimization methods in function spaces. 3. An algorithm for obtaining a global minimum of polynomial optimization problems generates a sequence of semidefinite programming problems. We gave sufficient conditions for such semidefinite programming problems to have strong duality properties.

Research Products

• [Journal Article] Real ideal and the duality of semidefinite programming for polynomial optimization (2013)
  • Author(s): Y. Sekiguchi, T. Takenawa, H. Waki
  • Journal Title: Japan Journal of Industrial and Applied Mathematics Volume: 30 Pages: 321-330
  • NAID: 10031185311
• [Journal Article] Real ideal and the duality of semidefinite programming for polynomial optimization (2013)
  • Author(s): Yoshiyuki Sekiguchi, Tomoyuki Takenawa and Hayato Waki
  • Journal Title: Japan Journal of Industrial and Applied Mathematics Volume: 20 Issue: 2 Pages: 321-330
  • DOI: 10.1007/s13160-013-0104-6
  • NAID: 10031185311
  • Peer Reviewed
• [Journal Article] An improved analysis of SRPT scheduling algorithm on the basis of functional optimization (2012)
  • Author(s): H. Fujiwara, Y. Sekiguchi
  • Journal Title: Information Processing Letters Volume: 112 Pages: 911-915
  • NAID: 120007100507
• [Journal Article] An improved analysis of SRPT scheduling algorithm on the basis of functional optimization (2012)
  • Author(s): Hiroshi Fujiwara, Yoshiyuki Sekiguchi
  • Journal Title: Information Processing Letters Volume: 112 Issue: 23 Pages: 911-915
  • DOI: 10.1016/j.ipl.2012.08.009
  • NAID: 120007100507
  • Peer Reviewed
• [Journal Article] Average-case competitive analyses for one-way trading (2011)
  • Author(s): H. Fujiwara, K. Iwama, Y. Sekiguchi
  • Journal Title: Journal of Combinatorial Optimization Volume: 21 Pages: 83-107
  • NAID: 120007100508
• [Journal Article] Average-Case Competitive Analyses for One-Way Trading (2011)
  • Author(s): H.Fujiwara, K.Iwama, Y.Sekiguchi
  • Journal Title: Journal of Combinatorial Optimization Volume: Vol.21 Pages: 83-107
  • NAID: 120007100508
  • Peer Reviewed
• [Journal Article] Exact estimates of the regularity modulus for infinite programming (2010)
  • Author(s): Y. Sekiguchi
  • Journal Title: Mathematical Programming Volume: 123 Pages: 253-263
• [Presentation] Real ideal and duality, Mathematics, Algorithms and Proofs 2012 (2012)
  • Author(s): Y. Sekiguchi
  • Organizer: Young researcher's session
  • Place of Presentation: Konstanz, Germany
  • Year and Date: 2012-09-18
• [Presentation] 凸代数幾何と最適化理論 (2012)
  • Author(s): 関口良行
  • Organizer: Mathematical Economics Monday Seminar in Keio University
  • Place of Presentation: 東京
  • Year and Date: 2012-04-16
• [Presentation] 凸代数幾何 と最適化理論 (2012)
  • Author(s): 関口 良行
  • Organizer: Mathematical Economics Monday Seminar in Keio University
  • Place of Presentation: 慶應大学
• [Presentation] Real ideal and duality of polynomial optimization (2012)
  • Author(s): Yoshiyuki Sekiguchi
  • Organizer: Young Researcher's session at Mathematics, Algorithms and Proofs 2012
  • Place of Presentation: University of Konstanz, Germany
• [Presentation] Real ideal and duality related to polynomial optimization, Optimization : theory (2011)
  • Author(s): Y. Sekiguchi
  • Organizer: algorithms and applications in economics
  • Place of Presentation: Barcelona
  • Year and Date: 2011-10-27
• [Presentation] Real ideal and duality related to polynomial optimization (2011)
  • Author(s): Yoshiyuki Sekiguchi
  • Organizer: Optimization : theory, algorithms and applications in economics
  • Place of Presentation: Barcelona, Spain
  • Year and Date: 2011-10-27
• [Presentation] 無限次元変分解析の理論とオンライン アルゴリズムにおける応用例 (2010)
  • Author(s): 関口良行
  • Organizer: Ramp シンポジウム
  • Place of Presentation: 名古屋
  • Year and Date: 2010-10-29
  • Invited
• [Presentation] 無限次元変分解析の理論とオンラインアルゴリズムにおける応用例 (2010)
  • Author(s): 関口良行
  • Organizer: Rampシンポジウム
  • Place of Presentation: 名古屋大学(愛知県)
  • Year and Date: 2010-10-29
• [Presentation] Real ideal and duality related to polynomial optimization (2010)
  • Author(s): Y. Sekiguchi
  • Organizer: Mathematical Economics Monday Seminar in Keio University
  • Place of Presentation: 東京
  • Year and Date: 2010-04-19