発表文献

発表文献

著書

1. 佐藤寛之，多様体上の最適化理論，オーム社，2024．（サポートページ）

2. H. Sato, Riemannian Optimization and Its Applications, Springer, 2021.
   (Lena Sembach 氏によるレビュー：Book Reviews, SIAM Review, 64(2), 503–513, 2022)
   (Anders Linnér 氏によるレビュー：Mathematical Reviews, October, 2022)

3. 情報工学編集委員会 編，理工系の基礎 情報工学，丸善出版，2018. （第6章を分担執筆）

プレプリント

1. K. Chen, E. H. Fukuda, and H. Sato, Nonlinear conjugate gradient method for vector optimization on Riemannian manifolds with retraction and vector transport, arXiv preprint, https://arxiv.org/abs/2307.15515.

2. Y. Yamakawa, H. Sato, and K. Aihara, Modified Armijo line-search in Riemannian optimization with reduced computational cost, arXiv preprint, https://arxiv.org/abs/2304.02197.

査読付き論文

1. M. Yamada and H. Sato, Conjugate gradient methods for optimization problems on symplectic Stiefel manifold, IEEE Control Systems Letters, 7,  2719–2724, 2023.

2. H. Sato, Riemannian optimization on unit sphere with p-norm and its applications, Computational Optimization and Applications, 85, 897–935, 2023.

3. H. Sakai, H. Sato, and H. Iiduka, Global convergence of Hager–Zhang type Riemannian conjugate gradient method, Applied Mathematics and Computation, 441, 127685 (12 pages), 2023.

4. H. Sato, Riemannian conjugate gradient methods: General framework and specific algorithms with convergence analyses, SIAM Journal on Optimization, 32(4), 2690–2717, 2022.

5. M. Kawai, H. Sato, and T. Shiohama, Topic model-based recommender systems and their applications to cold start problems, Expert Systems with Applications, 202, 117129 (19 pages), 2022.

6. Y. Yamakawa and H. Sato, Sequential optimality conditions for nonlinear optimization on Riemannian manifolds and a globally convergent augmented Lagrangian method, Computational Optimization and Applications, 81(2), 397–421, 2022.

7. X. Zhu and H. Sato, Cayley-transform-based gradient and conjugate gradient algorithms on Grassmann manifolds, Advances in Computational Mathematics, 47(4), 56 (28 pages), 2021.

8. J. Goto and H. Sato, Approximated logarithmic maps on Riemannian manifolds and their applications, JSIAM Letters, 13, 17–20, 2021.

9. X. Zhu and H. Sato, Riemannian conjugate gradient methods with inverse retraction, Computational Optimization and Applications, 77(3), 779–810, 2020.

10. K. Sato, H. Sato, and T. Damm, Riemannian optimal identification method for linear systems with symmetric positive-definite matrix, IEEE Transactions on Automatic Control, 65(11), 4493–4508, 2020.

11. K. Tsuyuzaki, H. Sato, K. Sato, and I. Nikaido, Benchmarking principal component analysis for large-scale single-cell RNA-sequencing, Genome Biology, 21:9 (17 pages), 2020.

12. H. Sato, H. Kasai, and B. Mishra, Riemannian stochastic variance reduced gradient algorithm with retraction and vector transport, SIAM Journal on Optimization, 29(2), 1444–1472, 2019.

13. H. Sato and K. Aihara, Cholesky QR-based retraction on the generalized Stiefel manifold, Computational Optimization and Applications, 72(2), 293–308, 2019.

14. 佐藤寛之，相原研輔，グラスマン多様体上の商構造を用いたニュートン法（Riemannian Newton's method on the Grassmann manifold exploiting the quotient structure），日本応用数理学会論文誌，28(4), 205–241, 2018. （日本応用数理学会2019年度論文賞（理論部門）受賞）

15. K. Sato and H. Sato, Structure-preserving H^2 optimal model reduction based on the Riemannian trust-region method, IEEE Transactions on Automatic Control, 63(2), 505–512, 2018.

16. K. Aihara and H. Sato, A matrix-free implementation of Riemannian Newton's method on the Stiefel manifold, Optimization Letters, 11(8), 1729–1741, 2017.

17. H. Sato, Riemannian Newton-type methods for joint diagonalization on the Stiefel manifold with application to independent component analysis, Optimization, 66(12), 2211–2231, 2017.

18. H. Sato and K. Sato, Riemannian optimal system identification algorithm for linear MIMO systems, IEEE Control Systems Letters, 1(2), 376–381, 2017.

19. 佐藤寛之，リーマン多様体上の最適化の理論と応用（Optimization on Riemannian manifolds and its applications），応用数理，27(1), 21–30, 2017.

20. H. Sato, A Dai–Yuan-type Riemannian conjugate gradient method with the weak Wolfe conditions, Computational Optimization and Applications, 64(1), 101–118, 2016.

21. H. Sato and T. Iwai, A new, globally convergent Riemannian conjugate gradient method, Optimization, 64(4), 1011–1031, 2015.

22. H. Sato, Joint singular value decomposition algorithm based on the Riemannian trust-region method, JSIAM Letters, 7, 13–16, 2015.

23. H. Sato and T. Iwai, Optimization algorithms on the Grassmann manifold with application to matrix eigenvalue problems, Japan Journal of Industrial and Applied Mathematics, 31(2), 355–400, 2014.

24. H. Sato and T. Iwai, A Riemannian optimization approach to the matrix singular value decomposition, SIAM Journal on Optimization, 23(1), 188–212, 2013.

査読付き国際会議プロシーディング

1. H. Sato, Simple acceleration of the Riemannian steepest descent method with the Armijo condition, Proceedings of the 60th IEEE Conference on Decision and Control (CDC 2021), 3836–3843, 2021.

2. H. Sato and K. Sato, Riemannian gradient-based online identification method for linear systems with symmetric positive-definite matrix, Proceedings of the 58th IEEE Conference on Decision and Control (CDC 2019), 3593–3598, 2019.

3. M. Kawai, T. Shiohama, and H. Sato, Practically feasible recommender systems for cold start problems, Proceedings of 2018 5th Asia-Pacific World Congress on Computer Science and Engineering (APWC on CSE), 103–112, 2018.

4. H. Kasai, H. Sato, and B. Mishra, Riemannian stochastic recursive gradient algorithm, Proceedings of the 35th International Conference on Machine Learning (ICML 2018), Proceedings of Machine Learning Research, 80, 2521–2529, 2018.

5. H. Kasai, H. Sato, and B. Mishra, Riemannian stochastic quasi-Newton algorithm with variance reduction and its convergence analysis, Proceedings of the 21st International Conference on Artificial Intelligence and Statistics (AISTATS 2018), Proceedings of Machine Learning Research, 84, 269–278, 2018.

6. M. Kawai, T. Shiohama, and H. Sato, Supervised-topic-model-based hybrid filtering for recommender systems, Proceedings of the 2nd International Conference on Big Data, Cloud Computing, and Data Science Engineering (BCD 2017), 266–271, 2017.

7. H. Sato and K. Sato, A new H^2 optimal model reduction method based on Riemannian conjugate gradient method, Proceedings of the 55th IEEE Conference on Decision and Control (CDC 2016), 5762–5768, 2016.

8. H. Kasai, H. Sato, and B. Mishra, Riemannian stochastic variance reduced gradient on Grassmann manifold, The 9th NIPS Workshop on Optimization for Machine Learning (OPT 2016), 2016. (4 pages)

9. H. Sato and K. Sato, Riemannian trust-region methods for H^2 optimal model reduction, Proceedings of the 54th IEEE Conference on Decision and Control (CDC 2015), 4648–4655, 2015.

10. H. Sato, Riemannian conjugate gradient method for complex singular value decomposition problem, Proceedings of the 53rd IEEE Conference on Decision and Control (CDC 2014), 5849–5854, 2014.

11. H. Sato and T. Iwai, A complex singular value decomposition algorithm based on the Riemannian Newton method, Proceedings of the 52nd IEEE Conference on Decision and Control (CDC 2013), 2972–2978, 2013.

査読なしプロシーディング等

1. 佐藤寛之，リーマン多様体上の最適化理論と勾配法について，第36回信号処理シンポジウム論文集，244–249, 2021.

2. 佐藤寛之，信号処理で用いられるリーマン多様体上の最適化手法について，第34回 回路とシステムワークショップ論文集，154–159, 2021.

3. H. Sato, Conjugate gradient methods on Riemannian manifolds, Oberwolfach Reports, 17(4), 1803–1806, 2021.

4. 佐藤寛之，リーマン多様体上の最適化問題に対する勾配法とその周辺，第31回RAMP数理最適化シンポジウム論文集，1–14, 2019.

5. 佐藤寛之，笠井裕之，Bamdev Mishra，リーマン多様体上の確率的最適化の発展，京都大学数理解析研究所講究録，2108, 168–176, 2019.

6. 佐藤寛之，幾何学的な最適化アルゴリズムとその応用，京都大学数理解析研究所講究録，2094, 55–64, 2018.

7. 吉井和佳，佐藤寛之，坂東宜昭，中村栄太，河原達也，独立低ランクテンソル分析：非負値性・低ランク性・独立性に基づくブラインド音源分離の統一理論，信学技報，118(284), 37–44, 2018.

8. 佐藤寛之，佐藤一宏，リーマン多様体上の最適化に基づく離散時間線形システム同定アルゴリズム，京都大学数理解析研究所講究録，2069, 153–165, 2018.

9. 佐藤寛之，笠井裕之，Bamdev Mishra，直交制約つき最適化問題に対するリーマン多様体上の確率的分散縮小勾配法，京都大学数理解析研究所講究録，2027, 135–143, 2017.

10. 佐藤寛之，相原研輔，一般化シュティーフェル多様体上のレトラクションとその効果的な実装について，京都大学数理解析研究所講究録，2027, 125–134, 2017.

11. 笠井裕之，佐藤寛之，Bamdev Mishra，Riemannian stochastic variance reduced gradient for large-scale machine learning，信学技報，116(171), 25–29, 2016.

12. 佐藤寛之，相原研輔，シュティーフェル多様体上のニュートン法とその収束性解析，京都大学数理解析研究所講究録，1981, 127–142, 2016.

13. A. Kitao, T. Shiohama, and H. Sato, Financial news classification based on topographic independent component analysis: Optimization on the Stiefel manifold, Proceedings of the 16th Applied Stochastic Models and Data Analysis International Conference, 403–415, 2015.

14. 佐藤寛之，シュティーフェル多様体上の信頼領域法の近似的同時特異値分解への応用，京都大学数理解析研究所講究録，1931, 161–168, 2015.

15. 佐藤寛之，シュティーフェル多様体上の同時対角化問題に対するニュートン法，京都大学数理解析研究所講究録，1879, 134–143, 2014.

16. 佐藤寛之，新しいリーマン多様体上の共役勾配法およびその収束性について，Hokkaido University Technical Report Series in Mathematics, 157, 109–112, 2013.

17. 佐藤寛之，岩井敏洋，リーマン多様体上の共役勾配法およびその特異値分解問題への応用，京都大学数理解析研究所講究録，1829, 39–53, 2013．

18. 佐藤寛之，リーマン多様体上の最適化アルゴリズムおよびその行列計算への応用，Hokkaido University Technical Report Series in Mathematics, 151, 97–100, 2012.

19. 佐藤寛之，リーマン多様体上の最適化アルゴリズムおよびその数値線形代数への応用，第3回白浜研究集会報告集，73–81, 2012.

20. 佐藤寛之，岩井敏洋，Optimization algorithms on the Grassmann and the Stiefel manifolds, 京都大学数理解析研究所講究録，1774, 1–17, 2012．

21. 佐藤寛之，岩井敏洋，グラスマン多様体上の最適化アルゴリズム，京都大学数理解析研究所講究録，1773, 165–176, 2012．

22. 佐藤寛之，行列多様体上の最適化アルゴリズム, Hokkaido University Technical Report Series in Mathematics, 148, 99–102, 2011.

解説記事

1. 佐藤寛之，最適化問題に対する微分幾何学的アプローチとロボット工学への応用，日本ロボット学会誌，41(6), 530–535, 2023.

2. 佐藤寛之，笠井裕之，リーマン多様体上の最適化の基本と最新動向，システム／制御／情報，62(1), 21–27, 2018.

3. 佐藤寛之，曲がった空間での最適化，オペレーションズ・リサーチ，60(9), 549–554, 2015.

その他の記事

1. 小川敬也，菊谷竜太，佐藤寛之，宮﨑牧人，シリーズ白眉対談15「最適化」，京都大学白眉センターだより，16, 2–5, 2018.

2. 佐藤寛之，Optimization on Riemannian manifolds: Combination of geometry and applied mathematics, 京都大学白眉センターだより，15, 13, 2018.

3. 佐藤寛之，SIAM Conference on Optimization (OP14) 参加報告，JSIAM Online Magazine, G1406E, 2014.

4. 佐藤寛之，日本応用数理学会 2012年度（第22回）年会参加報告，JSIAM Online Magazine, G1209A, 2013.

学位論文

博士論文

Riemannian optimization algorithms and their applications to numerical linear algebra, 2013年，京都大学．

修士論文

A new aspect of optimization algorithms on the Grassmann manifold, 2011年，京都大学．

卒業論文（特別研究報告書）

ハミルトン形式での繰り込み群方程式，2009年，京都大学．