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 |
Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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Research Institution | Tokyo University of Marine Science and Technology |
Principal Investigator |
|
Project Period (FY) |
2010-04-01 – 2014-03-31
|
Project Status |
Completed (Fiscal Year 2013)
|
Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
|
Keywords | 変分解析 / 最適化理論 / 関数解析 / 代数幾何 / 最適化問題 / 凸代数幾何 / 関数解析学 / 解析学 / 数理工学 / アルゴリズム |
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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Report
(5 results)
Research Products
(16 results)