Study on numerical methods for solving nonlinear optimization problems and their implementation
| Project/Area Number |
25330030
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Mathematical informatics
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| Research Institution | Tokyo University of Science |
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Principal Investigator |
YABE HIROSHI 東京理科大学, 理学部第一部数理情報科学科, 教授 (90158056)
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| Co-Investigator(Kenkyū-buntansha) |
成島 康史 横浜国立大学, 大学院国際社会科学研究院, 准教授 (70453842)
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| Research Collaborator |
M. Al-Baali
IGARASHI Yu
INABA Yousuke
OOTANI Ryousuke
OGASAWARA Hideho
KATO Atsushi
KOBAYASHI Hiroshi
SUGASAWA Kiyohisa
NAKATANI Satoshi
NAKAMURA Wataru
NAKAYAMA Shummin
HAYASHI Shunsuke
HARADA Kohei
HIRANO Tatsuya
YANAGIDA Kento
YAMASHITA Hiroshi
YAMAMOTO Akio
WATANABE Yu
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 最適化 / 非線形計画法 / 無制約最適化 / 制約条件付き最適化 / 非線形最適化 / 無制約最小化問題 / 制約条件付き最小化問題 / 準ニュートン法 / 逐次２次制約２次計画法 / 2次錐相補性問題 / 共役勾配法 / 外点法 |
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| Outline of Final Research Achievements |
We proposed new three-term conjugate gradient methods for solving large scale unconstrained optimization problems and new smoothing and scaling conjugate gradient methods for solving nonsmooth nonlinear equations. We showed the global convergence properties of our proposed methods and investigated their numerical performance. We also proposed a quasi-Newton pattern search method based on the Broyden family as one of direct search methods for unconstrained optimization problems and discussed its convergence property. In addition, we dealt with memoryless quasi-Newton methods for large scale unconstrained optimization problems. Furthermore, we proposed an inexact sequential qudratically constrained quadratic programming method of feasible directions for constrained optimization problems, and a primal-dual exterior point method with a primal-dual quadratic penalty function for nonlinear nonconvex optimization problems. We analyzed the convergence properties of the proposed methods.
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Report
(5 results)
Research Products
(42 results)
