2018 Fiscal Year Final Research Report
Optimization over the union of closed convex sets and its application to signal processing
| Project/Area Number |
26730128
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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 |
Soft computing
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2019-03-31
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| Keywords | 非凸最適化 / 信号処理 |
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| Outline of Final Research Achievements |
Many powerful signal processing algorithms have been proposed with the help of convex analysis. In this study, we introduce an optimization problem over the union of a finite family of closed convex sets, as a generalization of a convex optimization problem, and propose efficient algorithms for its several problem instances important in the context of signal processing. We confirm, by numerical experiments, that the proposed algorithms overcome existing algorithms based on convex optimization.
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| Free Research Field |
最適化工学，信号処理工学
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| Academic Significance and Societal Importance of the Research Achievements |
一般に，非凸最適化問題を解くことは非常に困難である．本研究では，工学的に重要ないくつかの非凸最適化問題が効率的に解けることを明らかにしており，その学術的意義は大きいと考えている．研究成果は理論的な基礎原理についての検討が中心となっており，社会実装のためには多くの課題が残されているが，携帯電話の通話品質改善を含む，様々な形で成果を社会へ還元したい．
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