[1] Ahn, K., Suarez, F.: Riemannian perspective on matrix factorization. arXiv preprint arXiv:2102.00937 (2021)
[2] Allen-Zhu, Z., Li, Y.: Neon2: Finding local minima via first-order oracles. Advances in Neural Information Processing Systems 31 (2018)
[3] Bhojanapalli, S., Jain, P.: Universal matrix completion. In: International Conference on Machine Learning, pp. 1881-1889. PMLR (2014)
[4] Bi, Y., Lavaei, J.: On the absence of spurious local minima in nonlinear low-rank matrix recovery problems. In: International Conference on Artificial Intelligence and Statistics, pp. 379-387. PMLR (2021)
[5] Bi, Y., Zhang, H., Lavaei, J.: Local and global linear convergence of general low-rank matrix recovery problems. In: Proceedings of 36th AAAI Conference on Artificial Intelligence (AAAI), Vancouver, Canada, pp. 1-9 (2022)
[6] Burer, S., Monteiro, R.D.: A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization. Mathematical Programming 95(2), 329-357 (2003)
[7] Candès, E.J., Li, X., Ma, Y., Wright, J.: Robust principal component analysis? Journal of the ACM (JACM) 58(3), 1-37 (2011)
[8] Candes, E.J., Li, X., Soltanolkotabi, M.: Phase retrieval via wirtinger flow: Theory and algorithms. IEEE Transactions on Information Theory 61(4), 1985-2007 (2015)
[9] Candes, E.J., Plan, Y.: Tight oracle inequalities for low-rank matrix recovery from a minimal number of noisy random measurements. IEEE Transactions on Information Theory 57(4), 2342-2359 (2011)
[10] Candès, E.J., Recht, B.: Exact matrix completion via convex optimization. Foundations of Computational mathematics 9(6), 717-772 (2009)
[11] Candès, E.J., Tao, T.: The power of convex relaxation: Near-optimal matrix completion. IEEE Transactions on Information Theory 56(5), 2053-2080 (2010)
[12] Cartis, C., Gould, N.I., Toint, P.L.: Adaptive cubic regularisation methods for unconstrained optimization. part i: motivation, convergence and numerical results. Mathematical Programming 127(2), 245-295 (2011)
[13] Chen, J., Liu, D., Li, X.: Nonconvex rectangular matrix completion via gradient descent without  $\ell_{2,\infty}$  regularization. IEEE Transactions on Information Theory 66(9), 5806-5841 (2020)
[14] Chen, Y., Chi, Y., Fan, J., Ma, C.: Gradient descent with random initialization: Fast global convergence for nonconvex phase retrieval. Mathematical Programming 176(1), 5-37 (2019)
[15] Chi, Y., Lu, Y.M., Chen, Y.: Nonconvex optimization meets low-rank matrix factorization: An overview. IEEE Transactions on Signal Processing 67(20), 5239-5269 (2019)
[16] Chou, H.H., Gieshoff, C., Maly, J., Rauhut, H.: Gradient descent for deep matrix factorization: Dynamics and implicit bias towards low rank. arXiv preprint arXiv:2011.13772 (2020)
[17] Ge, R., Jin, C., Zheng, Y.: No spurious local minima in nonconvex low rank problems: A unified geometric analysis. In: International Conference on Machine Learning, pp. 1233–1242. PMLR (2017)
[18] Ge, R., Lee, J.D., Ma, T.: Matrix completion has no spurious local minimum. Advances in Neural Information Processing Systems pp. 2981-2989 (2016)
[19] Hou, T.Y., Li, Z., Zhang, Z.: Fast global convergence for low-rank matrix recovery via riemanian gradient descent with random initialization. arXiv preprint arXiv:2012.15467 (2020)
[20] Jain, P., Meka, R., Dhillon, I.: Guaranteed rank minimization via singular value projection. Advances in Neural Information Processing Systems 23 (2010)
[21] Jain, P., Netrapalli, P., Sanghavi, S.: Low-rank matrix completion using alternating minimization. In: Proceedings of the forty-fifth annual ACM symposium on Theory of computing, pp. 665-674 (2013)
[22] Jin, C., Ge, R., Netrapalli, P., Kakade, S.M., Jordan, M.I.: How to escape saddle points efficiently. In: International Conference on Machine Learning, pp. 1724-1732. PMLR (2017)