A new paradigm in conic optimization: Optimization over the doubly nonnegative cone and software development

2014 Fiscal Year Final Research Report

• Project/Area Number: 23310099
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Social systems engineering/Safety system
• Research Institution: University of Tsukuba
• Principal Investigator: YOSHISE Akiko 筑波大学, システム情報系, 教授 (50234472)
• Co-Investigator(Kenkyū-buntansha): YAMAMOTO Yoshitsugu 筑波大学, システム情報系, 教授 (00119033) ; KUNO Takahito 筑波大学, システム情報系, 教授 (00205113) ; SHIGENO Maiko 筑波大学, システム情報系, 准教授 (40272687) ; HACHIMORI Masahiro 筑波大学, システム情報系, 准教授 (00344862)
• Co-Investigator(Renkei-kenkyūsha): FUJISAWA Katsuki 九州大学, 数理学研究院, 教授 (40303854) ; YAMASHITA Makoto 東京工業大学, 情報理工学研究科, 准教授 (20386824) ; WAKI Hayato 九州大学, 数理学研究院, 准教授 (00567597)
• Project Period (FY): 2011-04-01 – 2015-03-31
• Keywords: 錐最適化 / 二重非負値行列錐 / 半正定値緩和問題 / 共正値緩和問題 / 内点法 / 組合せ最適化

Outline of Final Research Achievements

The aim of this study is to propose new algorithms for solving a conic optimization problem, the doubly nonnegative optimization problem which is an optimization problem over the doubly nonnegative cone. Conic optimization includes a wide range of convex optimization problems, e.g., linear programs and semidefinite programs. There have been many studies that provide evidence of effectiveness of the semidefinite relaxation for combinatorial optimization problems and several commercial software packages for solving semidefinite programs have been developed. Our recent experiments showed that a tighter relaxation, the doubly nonnegative relaxation, is quite efficient for some classes of combinatorial optimization problems. However, in spite of its efficiency, it sometimes takes a quite long time to solve the doubly nonnegative programs using existing algorithms. To overcome the difficulty, we proposed an algorithm based on a new idea, implemented and improved it.

Free Research Field

数理最適化