1997 Fiscal Year Final Research Report Summary
Studies on Development and Synthesis of Efficient Algorithms for Optimization and Equilibrium Problems
| Project/Area Number |
08650079
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Engineering fundamentals
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| Research Institution | KYOTO UNIVERSITY |
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Principal Investigator |
FUKUSHIMA Masao Kyoto University, Grad. School of Engineering, Professor, 工学研究科, 教授 (30089114)
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| Co-Investigator(Kenkyū-buntansha) |
YAMAKAWA Eiki Takamatsu University, Faculty of Management, Lecturer, 経営学部, 講師 (20289333)
TAJI Kouichi Nara Institute of Science and Technology, Grad. School of Information Sci., Assi, 情報科学研究科, 助手 (00252833)
IBARAKI Satoru Kyoto University, Grad. School of Engineering, Assistant Professor, 工学研究科, 助手 (10252488)
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| Project Period (FY) |
1996 – 1997
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| Keywords | Optimization / Equilibrium Model / Algorithm / Variational Inequality Problem / Complementarity Problem |
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| Research Abstract |
Variational inequality and complementarity problems are fundamental problems that are very useful in formulating various equilibrium problems arising not only in engineering such as transportation, structural mechanics and operations reseach but also in social sciences such as economics. In this project, we have conducted research on those fundamental equilibrium problems with particular emphasis on the optimization reformulation approach that have recently attracted much attention in this field. The main results which have been obtained during the last two years are summarized as follows :
1.New approaches that reformulate variational inequality and complementarity problems as equivalent optimization problems have been proposed. Moreover novel algorithms that extend descent methods and Newton's method have been developed, and their effectiveness has been examined through extensive numerical experiments.
2.New parallel and decomposition methods for variational inequality and complementarity problems have been developed by meking use of the idea of operator splitting and matrix splitting.
3.New algorithms have been developed for solving mathematical program with equilibrium constraints for which a unified study has not been done so far.
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