2001 Fiscal Year Final Research Report Summary
Synthesis, Analysis and Algorithms of Optimization and Equilibrium Systems
| Project/Area Number |
11694151
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (B)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
System engineering
|
|---|
| Research Institution | KYOTO UNIVERSITY |
|---|
Principal Investigator |
FUKUSHIMA Masao Kyoto University, Graduate School of Informatics, Professor, 情報学研究科, 教授 (30089114)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
CHEN Xiaojun Shimane University, Interdisciplinary Faculty of Science and Engineering, Associate University, 総合理工学部, 助教授 (70304251)
YAMASHITA Nobuo Kyoto University, Graduate School of Informatics, Assistant Professor, 情報学研究科, 助手 (30293898)
|
|---|
| Project Period (FY) |
1999 – 2001
|
| Keywords | Optimization / Equilibrium model / Algorithm / Mathematical programming / Complementarity problem / Variation inequality problem / Parallel algorithm |
|---|
| Research Abstract |
Optimization is a fundamental concept in systems approach and a variety of methods have been developed and applied to practical problems. However, in order to deal with more complex problems that arise in engineering and social sciences, it is necessary to introduce the concept of hierarchical optimization or more generally optimization under equilibrium conditions, and construct a framework of effective methods for such problems. From this standpoint, the project have developed a number of approaches to the solution of various optimization and equilibrium problems. The obtained results are summarized as follows :
1. Efficient algorithms for solving the system of nonlinear equations, which constitutes the most fundamental class of equilibrium. Moreover efficient algorithms for unconstrained and constrained optimization problems have been developed.
2. The proximal point algorithm, which is one of the most basic approaches to optimization and equilibrium problems, has been studied, and some novel results on its desirable convergence properties have been established.
3. Various reformulation methods that enable us to solve equilibrium problems by means of optimization techniques have been developed.
4. Optimization problems involving equilibrium constraints have been studies in depth and a number of novel and remarkable results have been obtained.
|
