2006 Fiscal Year Final Research Report Summary
Research on Numerical Methods for Large-Scale Nonlinear Optimization Problems and their Applications to Software Codes
| Project/Area Number |
16510123
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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 |
Social systems engineering/Safety system
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| Research Institution | Tokyo University of Science |
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Principal Investigator |
YABE Hiroshi Tokyo University of Science, Faculty of Science, Professor, 理学部, 教授 (90158056)
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| Co-Investigator(Kenkyū-buntansha) |
YAMAKI Naokazu Shizuoka University, Faculty of Engineering, Professor, 工学部, 教授 (20120222)
NUMATA Kazumichi Tokyo University of Science, Faculty of Engineering, Associate Professor, 工学部, 助教授 (30106893)
OGASAWARA Hideho Tokyo University of Science, Faculty of Science, Junior Associate Professor, 理学部, 講師 (00231217)
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| Project Period (FY) |
2004 – 2006
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| Keywords | nonlinear optimization / nonlinear programming / semidefinite programming / conjugate gradient method / memory gradient method / quasi-Newton method / Newton method / primal-dual interior point method |
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| Research Abstract |
We have studied numerical methods for solving unconstrained and constrained optimization problems. Specifically, we have done the following.
(1) We have proposed new nonlinear conjugate gradient methods based on the modified secant and the multi-step secant conditions for solving large-scale unconstrained optimization problems. We have proved their global convergence properties. Our numerical experiments show that our proposed methods perform well.
(2) We have proposed a new memory gradient method for solving large-scale unconstrained optimization problems. We have proved their global convergence properties. Our numerical experiments show that our proposed method performs well.
(3) We have combined the limited memory quasi-Newton method, which was proposed by us, and the primal-dual interior point method to solve nonlinearly constrained optimization problems.
(4) We have analyzed local behavior of the primal-dual interior point method for degenerate nonlinear optimization problems.
(5) We have proposed primal-dual interior point methods for solving nonlinear second-order cone programming and nonlinear semidefinite programming problems. We have proved their global convergence properties by using primal-dual merit function within the framework of the line search strategy.
(6) We have proved the local and q-superlinear convergence of the quasi-Newton method with the Broyden family based on the modified secant condition for solving unconstrained optimization problems.
(7) We have dealt with the Barzilai-Borwein method to improve numerical performance of the steepest descent method, and we have proposed the extended Barzilai-Borwein method.
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