2000 Fiscal Year Final Research Report Summary
Studies on Reformulation Methods in Mathematical Programming
| Project/Area Number |
11650067
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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 |
MASAO Fukushima Kyoto University, Graduate School of Informatics, Professor, 情報学研究科, 教授 (30089114)
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| Co-Investigator(Kenkyū-buntansha) |
NOBUO Yamashita Kyoto University, Graduate School of Informatics, Assistant Professor, 情報学研究科, 助手 (30293898)
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| Project Period (FY) |
1999 – 2000
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| Keywords | Mathematical Programming / Optimization / Reformulation / Complementarity Problem / Variational Inequalities |
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| Research Abstract |
In the area of mathematical programming, much attention has recently been paid on the approach based on the idea of reformulation. Reformulation aims to transform a problem into an equivalent problem that is easier to deal with, and then solve it by using some efficient algorithms. A typical and classical example of such approaches is a penalty function method. Currently the reformulation approaches deal with not only optimization problems but also equilibrium problems such as complementarity problems and variational inequality problems. Moreover, with the diversification of the reformulation approaches, a variety of novel numerical methods such as smoothing methods and generalized Newton methods for nondifferentiable optimization problems and equations.
In this project, we have developed efficient and robust algorithms for solving some classes of mathematical programming problems, besed on some reformulaton methods with solid theoretical basis. The main results which have been obtained during the last two years are summarized as follows :
1. For nonlinear complementarity and variational inequality problems, we have proposed some reformulation-based methods that use functions such as the regularized gap function, Fischer-Burmeister function, and D-gap function. Moreoevr, we have intensively studied the mathematical program with equilibrium constraints, which is particularly important from the practical viewpoint, and developed some algorithms that have desirable properties.
2. Problems obtained by a reformulation method often has a certain type of nondifferentiability such as semismoothness. We have proposed some smoothing methods that further transform such a nonsmooth problem into a smooth one, and we have develop efficient numerical algorithms for solving the latter problem.
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