Previous Articles Next Articles
Hong Wang^{1}, Xin Liu^{2}, Xiaojun Chen^{1}, Yaxiang Yuan^{2}
Hong Wang, Xin Liu, Xiaojun Chen, Yaxiang Yuan. SNIG PROPERTY OF MATRIX LOWRANK FACTORIZATION MODEL[J]. Journal of Computational Mathematics, 2018, 36(3): 374390.
[1] Y. Koren, R. Bell, C. Volinsky, Matrix factorization techniques for recommender systems. IEEE, (2009), 3037. [2] S. Burer, R.D.C Monteiro, A nonlinear programming algorithm for solving semidefinite programs via lowrank factorization. Math. Program. Ser. B, 95(2013), 329357. [3] J. Cai, E. Candès, Z. Shen, A singular value thresholding algorithm for matrix completion. SIAM J. Optim., 20(2010), 19561982. [4] E. Candès, B. Recht, Exact matrix completion via convex optimization. Found. Comput. Math., 9(2008), 717772. [5] E. Candès, T. Tao, The power of convex relaxation:nearoptimal matrix completion. IEEE Trans. Inform. Theory, 56(2009), 20532080. [6] V. Chandrasekaran, S. Sanghavi, P.A. Parrilo, A.S. Willsky, Ranksparsity incoherence for matrix decomposition. SIAM J. Optim., 21(2011), 572596. [7] C. Chen, B. He, X. Yuan, Matrix completion via alternating direction methods. IMA J. Numer. Anal., 32(2012), 227245. [8] G. Takács, I. Pilászy, B. Németh, D. Tikk, Major components of the gravity recommendation system. ACM SIGKDD Explorations Newsletter, 9(2007), 8083. [9] E. Candès, X. Li, M. Soltanolkotabi, Phase retrieval via Wirtinger flow:Theory and algorithms. IEEE Trans. on Inform. Theory, 61(2015), 19852007. [10] G. Rong, Jason D. Lee and T. Ma, Matrix Completion has No Spurious Local Minimum. arXiv:1605.07272 [11] D. Goldfarb, S. Ma, Convergence of fixedpoint continuation algorithms for matrix rank minimization. Found. Comput. Math., 11(2011), 183210. [12] M. Hardt, Understanding alternating minimization for matrix completion. arXiv:1312.0925. [13] P. Jain, P. Netrapalli, S. Sanghavi, Lowrank matrix completion using alternating minimization. in Proc. 45th Symposium on Theory of Computing, 2013, pp. 665674. [14] M. Journe, F. Bach, P.A. Absil, R. Sepulchre, Lowrank optimization on the cone of positive semidefinite matrices. SIAM J. Optim., 20(2010), 23272351. [15] X. Liu, Z. Wen, Y. Zhang, Limited memory block Krylov subspace optimization for computing dominant singular value decompositions. SIAM J. Sci. Comput., 35(2013), A1641A1668. [16] X. Liu, Z. Wen, Y. Zhang, An efficient GaussNewton algorithm for symmetric lowrank product matrix approximations. SIAM J. Optim, 25(2015), 1571?608. [17] Z. Lu, Y. Zhang, Penalty decomposition methods for rank minimization. under review. [18] S. Ma, D. Goldfarb, L. Chen, Fixed point and Bregman iterative methods for matrix rank minimization. Math. Program. Ser. A, 128(2011), 321353. [19] B. Mishra, G. Meyer, F. Bach, R. Sepulchre, Lowrank optimization with trace norm penalty. SIAM J. Optim., 23(2013), 21242149. [20] K. Murty, S. Kabadi, Some NPcomplete problems in quadratic and nonlinear programming. Math. Program., 39(1987), 117129. [21] Singh, P. Ajit, Gordon, J. Geoffrey, A unified view of matrix factorization models. Springer, 358373(2008). [22] R. Sun, Z. Luo, Guaranteed matrix completion via nonconvex factorization.arXiv:1411.8003. [23] B. Recht, M. Fazel, A. Parrilo, Guaranteed minimumrank solutions of linear matrix equations via nuclear norm minimization. SIAM Review, 52(2010), 471501. [24] S. Oymak, K. Mohan, M. Fazel, B. Hassibi, A simplified approach to recovery conditions for low rank matrices. IEEE International Symposium on Information Theory(2011). [25] S. Oymak, B. Hassibi, New null space results and recovery thresholds for matrix rank minimization. IEEE International Symposium on Information Theory(2011). [26] Z. Wang, M. Lai, Z. Lu, J. Ye, Orthogonal rankone matrix pursuit for matrix completion. under review. [27] Z. Wen, C. Yang, X. Liu, Y. Zhang, Tracepenalty minimization for largescale eigenspace computation. under review at J. Sci. Comput.. [28] Z. Wen, W. Yin, Y. Zhang, Solving a lowrank factorization model for matrix completion by a nonlinear successive overrelaxation algorithm, Math. Program. Comput., 4(2012), 333361. [29] Z. Zhu, A. So, Y. Ye, Fast and nearoptimal matrix completion via randomized basis pursuit. Proceed. of the Fifth International Congress of Chinese Mathematicians, ser. AMS/IP Studi. Adv. Math., 51(2009), 859882. 
[1]  Yanping Wang, Chuanlong Wang . The SecondOrder Optimality Conditions for Variable Programming [J]. Journal of Computational Mathematics, 2008, 26(5): 756766. 
[2]  Wen Yu SUN,Raimundo.J.B. Sampaio,M.A.B. Candido. PROXIMAL POINT ALGORITHM FOR MINIMIZATION OF DC FUNCTION [J]. Journal of Computational Mathematics, 2003, 21(4): 451462. 
[3]  Xiong Da CHEN,Ya Xiang YUAN. ON MAXIMA OF DUAL FUNCTION OF THE CDT SUBPROBLEM [J]. Journal of Computational Mathematics, 2001, 19(2): 113124. 
Viewed  
Full text 


Abstract 

