2013 Fiscal Year Final Research Report
Reconstruction of variational analysis through industrial mathematics
| Project/Area Number |
22740057
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Tokyo University of Marine Science and Technology |
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Principal Investigator |
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | 変分解析 / 最適化理論 / 関数解析 / 代数幾何 |
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| Research Abstract |
We considered quantitative analysis of metric regularity in variational analysis and inequality systems on Banach spaces by functional analytic methods. In addition, we studied theoretical properties of a algorithm for obtaining a global minimum of polynomial optimization problems. Our main results are the following:
1. We gave a formula for modulus of regularity of inequality systems on the space of continuous function. 2. We improved estimates of performance of an SRPT scheduling algorithm by optimization methods in function spaces. 3. An algorithm for obtaining a global minimum of polynomial optimization problems generates a sequence of semidefinite programming problems. We gave sufficient conditions for such semidefinite programming problems to have strong duality properties.
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