Project/Area Number  06650443 
Research Category 
GrantinAid for Scientific Research (C).

Research Field 
System engineering

Research Institution  Nara Institute of Science and Technology 
Principal Investigator 
福嶋 雅夫 奈良先端科学技術大学院大学, 教授
FUKUSHIMA Masao Nara Institute of Science and Technology, Grad.School of Information Sci., Professor, 情報科学研究科, 教授 (30089114)

CoInvestigator(Kenkyūbuntansha) 
TAJI Kouichi Nara Institute of Science and Technology, Grad.School of Information Sci., Resea, 情報科学研究科, 助手 (00252833)
ISHIDA Yoshiteru Nara Institute of Science and Technology, Grad.School of Information Sci., Assoc, 情報科学研究科, 助教授 (80159748)

Project Fiscal Year 
1994 – 1995

Project Status 
Completed(Fiscal Year 1995)

Budget Amount *help 
¥1,500,000 (Direct Cost : ¥1,500,000)
Fiscal Year 1995 : ¥600,000 (Direct Cost : ¥600,000)
Fiscal Year 1994 : ¥900,000 (Direct Cost : ¥900,000)

Keywords  Largescale system / Optimization / Convex Analysis / Algorithm / 大規模システム / 最適化 / 凸解析 / アルゴリズム 
Research Abstract 
In this project, we have conducted research on system optimization methods, aiming at establishing the theoretical foundation based on convex analysis and, in particular, developing new algorithms suited to implementation on a parallel computer. The main results which have been obtained during the last two years are summarized as follows : 1. Novel algorithms based on the alternating direction method of multipliers have been proposed for convex programming and applied to various problems such as transportation problems and multicommodity flow problems. Their practical effectiveness has been confirmed by extensive numerical experiments on a parallel computer. Moreover, extension of those algorithms to variational inequality problems have been proposed and shown to be effectively applicable to traffic equilibrium problems. 2. New implementation strategies of the primaldual proximal point algorithm have been proposed for convex programming problems. The primaldual proximal point algorithm has also been applied to variational inequality problems and its parallel implementation is shown to some problems with certain separable structure. 3. Introducing a trust region strategy, a new proximal point algorithm with descent property has been proposed and its practical efficiency has been verified through numerical experiments on a parallel computer. 4. New parallel algorithms for solving quadratic programming problems and linear complementarity problems have been proposed. Both theoretical and practical effectiveness have been studied in depth. 5. Optimization approaches to variational inequality and nonlinear complementarity problems have been explored. The obtained results are expected to play an important role in the development of efficient algorithms for solving those problems.
