2018 Fiscal Year Final Research Report
Development of fast algorithms for semi-infinite programs with conic constraints and application to practical problems
| Project/Area Number |
15K15943
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Mathematical informatics
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| Research Institution | Institute of Physical and Chemical Research (2017-2018)
Tokyo University of Science (2015-2016) |
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Principal Investigator |
Okuno Takayuki 国立研究開発法人理化学研究所, 革新知能統合研究センター, 研究員 (70711969)
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| Research Collaborator |
Fukushima Masao
Hayashi Shunsuke
Yamashita Nobuo
Tanaka Mirai
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Keywords | 半無限最適化 / 錐最適化 / 非凸最適化 / アルゴリズム / 交換法 / 主双対パス追跡法 / 半正定値錐, 2次錐 / DC最適化 |
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| Outline of Final Research Achievements |
In this research project, we studied optimization problems which can be expressed as the problem of minimizing a given real-valued function subject to inequality and equality constraints. Particularly, we focus on a semi-infinite conic program (SICP) which is a special class of optimization problems having infinitely many inequality constraints (semi-infinite constraints) together with conic constraints.
Our main contribution was to propose several algorithms for finding KKT points of SICPs or closely related optimization problems, where a KKT point is a solution satisfying certain technical conditions related to the problems under consideration. We analyzed conditions under which the proposed algorithms output KKT points. Moreover, we actually implemented the proposed algorithms and showed their efficiency via several numerical experiments.
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| Free Research Field |
連続最適化, 数理工学
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| Academic Significance and Societal Importance of the Research Achievements |
半無限錐計画問題は, 有限次元インパルス応答フィルター設計などの工学上多くの重要な諸問題から自然なモデル化を通して出現することが多い. したがって半無限錐計画問題を効率的に解く方法論を立脚し、その解を与えることは, そうした諸問題を効率的な解決, もしくはその糸口を与えることになりうる.
これまで錐制約や半無限制約を別々にもった最適化問題の研究は深く行われてきた. 一方, その両方を兼ね揃えた半無限錐計画問題を解くアルゴリズムの設計のためには二つの構造の特徴をうまく活かすことが重要であるものの, そうした研究は少ない. その意味で本研究成果で得られた手法とその理論は意義があると考えられる.
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