Developments of primal and dual sparse optimization models and their efficient solution methods
| Project/Area Number |
17K00032
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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 | Kyoto University |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2022-03-31
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| Project Status |
Completed (Fiscal Year 2021)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | スパース最適化 / 双対問題 / 多目的最適化 / 乗数法 / ロバスト最適化 / 近接勾配法 / 凸最適化 / 情報基礎 / 応用数学 / 最適化 |
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| Outline of Final Research Achievements |
In this study, we consider primal-dual sparse optimization models that have sparse primal and dual solutions for large-scale optimization problems in data analysis, machine learning, and financial engineering. We develop efficient solution methods for them. We presented two-type of formulations of the primal-dual sparse models, and proposed solution methods based on the method of multipliers and the implicit programming approach. Furthermore, we applied our findings in this study to multi-objective optimization, the Levenberg-Marquardt method, and multi-valued support vector machines.
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| Academic Significance and Societal Importance of the Research Achievements |
データ解析，機械学習，金融工学などであらわれる数理最適化問題は年々大規模化している．これまでは，精度の高い解を求めることを諦めて，現実的な時間内で妥当な解を求めていた．本研究では，スパース性を利用して，必要な性質を保存したまま問題規模の縮小が可能なことを示している．この結果は，高精度の解が必要となる応用において大きな意義がある．
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Report
(6 results)
Research Products
(26 results)
