2001 Fiscal Year Final Research Report Summary
Duality Theory and Solution Methods for Hierarchical Optimization Problems
| Project/Area Number |
11680452
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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 |
社会システム工学
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| Research Institution | Sophia University |
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Principal Investigator |
ISHIZUKA Yo Sophia University, Faculty of Science and Technology, Associate Professor, 理工学部, 助教授 (90176206)
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| Project Period (FY) |
1999 – 2001
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| Keywords | Hierarchical Optimization Problem / Duality / Solution Methods / Production Systems / Buffer Allocation Problem / Second order cone Programming / DC Functions |
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| Research Abstract |
The results of this research are classified into the following two categories :
1.Formulations and solution methods for optimal design problems of production systems that can be formulated as optimization problems including "max" operations in their constraints.
2.Theoretical contributions toward developing the duality theory for hierarchical optimization problems.
As for 1., we have shown that many "sample-path optimization" problems of production systems with stochastic variabilities can be formulated as the optimization problems with "max" operations, and developed solution methods for them. In case when the design variables of the production system are discrete such as buffer allocations or kanban allocations, we used the genetic algorithm. While, for the case of continuous design variables such as service capacity allocations, we developed a solution method via second order cone programming,
As for the theoretical contributions, we have obtained :
(1) Some notions of optimal solutions of hierarchical optimization problems with nonsingleton lower-level's reaction set ;
(2) First-order and second-order characterizations of optimal solutions of hierarchical optimization problems ;
(3) Dual representations of hierarchical optimization problems by use of the conjugate of the convex functions.
Especially, the dual representation scheme is derived from a Farkas type theorem for DC (Difference Convex) inequality systems, and is a major result of this study.
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