[9] Simon S Du, Chi Jin, Jason D Lee, Michael I Jordan, Aarti Singh, and Barnabas Poczos. Gradient descent can take exponential time to escape saddle points. Advances in Neural Information Processing Systems, 30, 2017.
[10] Arpita Gang and Waheed U Bajwa. Fast-pca: A fast and exact algorithm for distributed principal component analysis. IEEE Transactions on Signal Processing, 70:6080-6095, 2022.
[11] Arpita Gang and Waheed U. Bajwa. A linearly convergent algorithm for distributed principal component analysis. Signal Processing, 193:108408, 2022.
[12] Arpita Gang, Bingqing Xiang, and Waheed U. Bajwa. Distributed principal subspace analysis for partitioned big data: Algorithms, analysis, and implementation. IEEE Transactions on Signal and Information Processing over Networks, 7:699-715, 2021.
[13] G. Gidel, F. Bach, and S. Lacoste-Julien. Implicit regularization of discrete gradient dynamics in linear neural networks. In Advances in Neural Information Processing Systems, volume 32, pages 3202-3211, 2019.
[14] D. Hajinezhad and M. Hong. Perturbed proximal primal-dual algorithm for nonconvex nonsmooth optimization. Math. Program., Ser. B, 176:207-245, 2019.
[15] M Hong, D. Hajinezhad, and M. Zhao. Prox-PDA: The proximal primal-dual algorithm for fast distributed nonconvex optimization and learning over networks. In Proc. of the 34th International Conference on Machine Learning (ICML 2017), volume 70, pages 1529-1538, 2017.
[16] M. Hong, J. D. Lee, and M. Razaviyayn. Gradient primal-dual algorithm converges to second-order stationary solution for nonconvex distributed optimization over networks. In International Conference on Machine Learning, pages 2014-2023, 2018.
[17] M. Hong, S. Zeng, J. Zhang, and H. Sun. On the divergence of decentralized nonconvex optimization. SIAM Journal on Optimization, 32(4):2879-2908, 2022.
[18] Charikleia Iakovidou and Ermin Wei. On the convergence of near-dgd for nonconvex optimization with second order guarantees. In 2021 60th IEEE Conference on Decision and Control (CDC), pages 259-264, 2021.
[19] Yuchen Jiao and Yuantao Gu. Communication-efficient decentralized subspace estimation. IEEE Journal of Selected Topics in Signal Processing, 16(3):516-531, 2022.
[20] Jikai Jin, Zhiyuan Li, Kaifeng Lyu, Simon Du, and Jason Lee. Understanding incremental learning of gradient descent: A fine-grained analysis of matrix sensing. arXiv prespring, arXiv:2301.11500, 2023.
[21] D. S. Kalogerias and A. P. Petropulu. Matrix completion in colocated mimo radar: Recoverability, bounds and theoretical guarantees. IEEE Transactions on Signal Processing, 62(2):309-321, 2013.
[22] Q. Li, Z. Zhu, and G. Tang. The non-convex geometry of low-rank matrix optimization. Inf. Inference, 8(1):51–96, 2019.
[23] Weijian Li, Xianlin Zeng, Yiguang Hong, and Haibo Ji. Distributed design for nuclear norm minimization of linear matrix equations with constraints. IEEE Transactions on Automatic Control, 66(2):745-752, 2020.
[24] Songtao Lu, Jason D. Lee, Meisam Razaviyayn, and Mingyi Hong. Linearized admm converges to second-order stationary points for non-convex problems. IEEE Transactions on Signal Processing, 69:4859-4874, 2021.
[25] Marie Maros and Gesualdo Scutari. Dgd^2: A linearly convergent distributed algorithm for high-dimensional statistical recovery. In S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, and A. Oh, editors, Advances in Neural Information Processing Systems, volume 35, pages 3475-3487. Curran Associates, Inc., 2022.