1995 Fiscal Year Final Research Report Summary
Studies on Optimization Algorithms for Large-Scale Systems Based on Convex Analysis
| Project/Area Number |
06650443
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
System engineering
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| Research Institution | Nara Institute of Science and Technology |
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Principal Investigator |
FUKUSHIMA Masao Nara Institute of Science and Technology, Grad.School of Information Sci., Professor, 情報科学研究科, 教授 (30089114)
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| Co-Investigator(Kenkyū-buntansha) |
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)
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| Project Period (FY) |
1994 – 1995
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| Keywords | Large-scale system / Optimization / Convex Analysis / Algorithm |
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| 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 multi-commodity 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 primal-dual proximal point algorithm have been proposed for convex programming problems. The primal-dual 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.
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