Developing Global Optimization Methods for Discrete DC Function Minimization Problems

2018 Fiscal Year Final Research Report

• Project/Area Number: 15K00030
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical informatics
• Research Institution: Tokyo Institute of Technology
• Principal Investigator: Shioura Akiyoshi 東京工業大学, 工学院, 准教授 (10296882)
• Project Period (FY): 2015-04-01 – 2019-03-31
• Keywords: 離散凸関数 / 離散凸解析 / 離散DC関数 / 離散最適化 / アルゴリズム

Outline of Final Research Achievements

In this research project, we dealt with the discrete DC-function minimization problem, and made an attempt to detect a class of well-solved problems and to devise approximation algorithms with theoretical guarantee. We also aimed at better understanding the structure of M-convex and L-convex functions, and re-consider the minimization problems of M-convex and L-convex functions. For the problems, we improved the existing algorithms as well as their analysis for the running time. Furthermore, we investigated the problems that are in between the unconstrained discrete convex function minimization problem and the discrete DC-function minimization, clarified the structure of the problems, and devised fast algorithms for the problems.

Free Research Field

離散最適化

Academic Significance and Societal Importance of the Research Achievements

本研究課題で得られた成果により，高速に解くことのできる離散最適化問題の新たな枠組みを提示できた．また，これまで高速なアルゴリズムが知られていなかった様々な離散最適化問題に対して高速なアルゴリズムを提供できたとともに，高速なアルゴリズムが存在していた問題に対しては，より高速なアルゴリズムを提供できた．これらの研究成果が直接，現実の問題に適用できるとは限らないが，現実の複雑な問題を高速に解くことを目指す際，本研究課題で得られたアルゴリズムの活用が期待される．