Project/Area Number  08680478 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
社会システム工学

Research Institution  THE INSTITUTE OF STATISTICAL MATHEMATICS 
Principal Investigator 
MIZUNO Shinji ISM, DEPT.OF PREDICTION AND CONTROL, 予測制御研究系, 助教授 (90174036)

CoInvestigator(Kenkyūbuntansha) 
ITO Satoshi ISM, CENTER FOR DEV.OF STAT.COMP, 計算開発センター, 助教授 (50232442)
TSUCHIYA Takashi ISM, DEPT.OF PREDICTION AND CONTROL, 予測制御研究系, 助教授 (00188575)

Project Fiscal Year 
1996 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥2,700,000 (Direct Cost : ¥2,700,000)
Fiscal Year 1998 : ¥900,000 (Direct Cost : ¥900,000)
Fiscal Year 1997 : ¥900,000 (Direct Cost : ¥900,000)
Fiscal Year 1996 : ¥900,000 (Direct Cost : ¥900,000)

Keywords  OPTIMIZATION / SOCIAL SYSTEM / INTERIORPOINT METHOD / LlNEAR PROGRAMMING / 最適化 / 社会システム / 内点法 / 線形計画問題 / 半正定値計画問題 / 相補性問題 
Research Abstract 
We have performed a basic research on the interior point methods for solving optimization problems in social systems. In this year, our research mainly devoted to the development of interior point methods for linear programming and semidefinite programming, and devoted to the analysis of the global convergence and the local convergence of these methods. Most of the optimization problems iii social systems could be modeled as mathematical programming problems. The linear programming problem is the most fundamental mathematical programming problem. We performed two important research on the interiorpoint methods for linear programming. Firstly, in order to speed up the local convergence of interior point methods, we investigated an algorithm which trace the central path in high degree. As a result of this research, we proposed a high order infeasible interior point algorithm. Secondly, we are interested in the problem to get an initial interior point to perform an algorithm, For this purpose, we investigated two selfdual systems for linear programming, which have trivial initial points. We studied not only linear programming, but also convex programming, semidefinite programming, and semiinfinite programming. There are many search directions in interiorpoint methods for solving semidefinite programming problems. We investigated a selfdual subfamily of such directions. We also studied interiorpoint methods for solving linear and quadratic semiinfinite programming problems and proposed a dualparameterization algorithm for convex semiinfinite programming.
