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We derive a stochastic gradient algorithm for semidefinite optimization using randomization techniques.
On estimating the largest eigenvalue with the Lanczos algorithm
BN Parlett, H. Simon, and LM Stringer · 1982
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Problem complexity and method efficiency in optimization
A. Nemirovsky and D. Yudin · 1983
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The convergence behavior of Ritz values in the presence of close eigenvalues
A. Van der Sluis and HA Van der Vorst · 1987
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Matrix computation
G.H. Golub and C.F. Van Loan · 1990
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Matrix perturbation theory
G.W. Stewart and J. Sun · 1990
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Topics in matrix analysis
R.A. Horn and C.R. Johnson · 1991
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Estimating the largest eigenvalue by the power and Lanczos algorithms with a random start
J. Kuczynski and H. Wozniakowski · 1992
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Acceleration of stochastic approximation by averaging
BT Polyak and AB Juditsky · 1992
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Numerical methods for large eigenvalue problems
Y. Saad · 1992
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Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming
M.X. Goemans and D.P. Williamson · 1995
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ARPACK: Solution of Large-scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods
R.B. Lehoucq, D.C. Sorensen, and C. Yang · 1998
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LAPACK Users’ guide
E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, et al · 1999
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Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays
A. Alon, N. Barkai, D. A. Notterman, K. Gish, S. Ybarra, D. Mack, and A. J. Levine · 1999
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A rank minimization heuristic with application to minimum order system approximation
M. Fazel, H. Hindi, and S. Boyd · 2001
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On the distribution of the largest eigenvalue in principal components analysis
I.M. Johnstone · 2001
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Matrix Algorithms Vol. II: Eigensystems
G.W. Stewart · 2001
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Approximating Subdifferentials by Random Sampling of Gradients
J. Burke, A. Lewis, and M. Overton · 2002
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Learning the kernel matrix with semi-definite programming
G. R. G. Lanckriet, N. Cristianini, P. Bartlett, L. El Ghaoui, and M. I. Jordan · 2002
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Patterns in eigenvalues: The 70th Josiah Willard Gibbs lecture
P. Diaconis · 2003
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Orthogonal eigenvectors and relative gaps
Inderjit S. Dhillon and Beresford N. Parlett · 2003
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Fast monte-carlo algorithms for finding low-rank approximations
A. Frieze, R. Kannan, and S. Vempala · 2004
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Consistency of trace norm minimization
F. Bach · 2007
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A direct formulation for sparse PCA using semidefinite programming
A. d’Aspremont, L. El Ghaoui, M.I. Jordan, and G. R. G. Lanckriet · 2007
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Fast Monte Carlo algorithms for matrices I: Approximating matrix multiplication
P. Drineas, R. Kannan, and M.W. Mahoney · 2007
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Tracy-Widom limit for the largest eigenvalue of a large class of complex sample covariance matrices
N. El Karoui · 2007
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Gradient methods for minimizing composite objective function
Y. Nesterov · 2007
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A randomized method for solving semidefinite programs
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A Robust Gradient Sampling Algorithm for Nonsmooth, Nonconvex Optimization
J.V. Burke, A.S. Lewis, and M.L. Overton · 2005
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First-order methods for sparse covariance selection
A. d’Aspremont, O. Banerjee, and L. El Ghaoui · 2006
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Fast Monte Carlo Algorithms for Matrices II: Computing a Low-Rank Approximation to a Matrix
P. Drineas, R. Kannan, and M.W. Mahoney · 2006
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The design and implementation of the MRRR algorithm
I.S. Dhillon, B.N. Parlett, and C. Vömel · 2006
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The fastest mixing Markov process on a graph and a connection to a maximum variance unfolding problem
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B. T. Polyak and P. S. Shcherbakov · 2007
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Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization
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Exact matrix completion via convex optimization
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Solving variational inequalities with Stochastic Mirror-Prox algorithm
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Stochastic approximation approach to stochastic programming
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Spectral algorithms
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Primal-dual subgradient methods for convex problems
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