Unified Optimization Theory by Discrete Convex Paradigm

2014 Fiscal Year Final Research Report

• Project/Area Number: 21360045
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Engineering fundamentals
• Research Institution: The University of Tokyo
• Principal Investigator: MUROTA Kazuo 東京大学, 情報理工学(系)研究科, 教授 (50134466)
• Co-Investigator(Renkei-kenkyūsha): TAMURA Akihisa 慶應義塾大学, 理工学部, 教授 (50217189) ; IWATA Satoru 東京大学, 大学院情報理工学系研究科, 教授 (00263161) ; SHIOURA Akiyoshi 東北大学, 情報科学研究科, 准教授 (10296882) ; MORIGUCHI Satoko 首都大学東京, 社会科学研究科, 准教授 (60407351) ; KAKIMURA Naonori 東京大学, 大学院総合文化研究科, 特任講師 (30508180) ; KOBAYASHI Yusuke 東京大学, 大学院情報理工学系研究科, 助教 (40581591) ; TSUCHIMURA Nobuyuki 関西学院大学, 理工学部, 教育技術職員 (20345119)
• Project Period (FY): 2009-04-01 – 2015-03-31
• Keywords: 離散最適化 / 凸関数 / 双対性 / 劣モジュラ関数 / マトロイド

Outline of Final Research Achievements

This research integrated the theory and application of optimization in various fields of engineering and social sciences by Discrete Convex Paradigm. We analyzed the theory and applications of discrete convex analysis, to clarify the mutual relationship of the individual mathematical techniques and problems in applications, from three aspects of the continuous-discrete axis, the convex-nonconvex axis, and the fields-transversal axis. Also we conducted research from three aspects of mathematical deepening, applications development, and software development, and achieved the new developments in Discrete Convex Paradigm. In particular, mathematical deepening includes the results of detailed analysis in L-convex function minimization algorithm and presentation of a framework of discrete DC programming.

Free Research Field

数理工学