1991 Fiscal Year Final Research Report Summary
Studies on parallel algorithms for mathematical programming
| Project/Area Number |
02680025
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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 |
Informatics
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| Research Institution | Kyoto University |
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Principal Investigator |
FUKUSHIMA Masao Kyoto Univ., Fac. of Eng., Assoc. Professor, 工学部, 助教授 (30089114)
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| Co-Investigator(Kenkyū-buntansha) |
NAGAMOCHI Hiroshi Kyoto Univ., Fac. of Eng., Assistant Professor, 工学部, 助手 (70202231)
OHNISHI Masamitsu Kyoto Univ., Fac. of Eng., Assistant Professor, 工学部, 助手 (10160566)
IBARAKI Toshihide Kyoto Univ., Fac. of Eng., Professor, 工学部, 教授 (50026192)
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| Project Period (FY) |
1990 – 1991
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| Keywords | Mathematical Programming / parallel algorithm / optimization |
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| Research Abstract |
In this project, we have conducted research on parallel algorithms for solving mathematical programming problems. The main results which have been obtained for the last two years are summarized as follows :
1. When the objective function is represented as the sum of a continuously differentiable function and a convex function which is separable with respect to individual variables, the problem can be solved using a parallelizable iteractive method such as projection and Jacobi methods. This type of problems can also be obtained by formulating a dual of a general convex programming problem, even if the latter problem does not have any separable structure. Therefore this approach is effective for a wide class of problems. Based on this idea, we have unified several existing algorithms and also proposed a new parallel algorithm for solving general convex programming problems.
2. Many decomposition methods have been proposed for ninlinear programming problems with certain separable structure. But those methods are not necessarily efficient from a practical viewpoint. We have proposed some improved decomposition algorithms and examined their effectiveness by numerical experiments.
3. We have found that the dual of a separable convex programming problem can be transformed into a problem which can effectively be solved by the alternating direction method of multipliers. The resulting algorithm turns out to be particularly suitable for parallel computation. The results of numerical experiments with the algorithm on a parallel computer are very encouraging.
4. As a foundation for the future research, we have studied such problems as network programming problems and variational inequality problems, and developed some algorithms for those problems. To investigate the possibility of developing parallel algorithms for such problems is a topic for future research.
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