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Semidefinite programs (SDP) are important in learning and combinatorial optimization with numerous applications.
Some applications of optimization in matrix theory
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Interior-point polynomial algorithms in convex programming , volume 13
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A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization
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K. Krishnan and J. E. Mitchell · 2003
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Learning the kernel matrix with semidefinite programming
G. R. Lanckriet, N. Cristianini, P. Bartlett, L. E. Ghaoui, and M. I. Jordan · 2004
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Fast algorithms for approximate semidefinite programming using the multiplicative weights update method
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S. Burer and R. D. Monteiro · 2005
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Cubic regularization of newton method and its global performance
Y. Nesterov and B. T. Polyak · 2006
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E. Hazan · 2008
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Exact matrix completion via convex optimization
E. J. Candès and B. Recht · 2009
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Fast global convergence rates of gradient methods for high-dimensional statistical recovery
A. Agarwal, S. Negahban, and M. J. Wainwright · 2010
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Low-rank optimization on the cone of positive semidefinite matrices
M. Journée, F. Bach, P.-A. Absil, and R. Sepulchre · 2010
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Dictionary learning and tensor decomposition via the sum-of-squares method
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R. Ge, F. Huang, C. Jin, and Y. Yuan · 2015
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A. S. Bandeira, N. Boumal, and V. Voroninski · 2016
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Faster projection-free convex optimization over the spectrahedron
D. Garber · 2016
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Sublinear time algorithms for approximate semidefinite programming
D. Garber and E. Hazan · 2016
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Matrix completion has no spurious local minimum
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B. Recht, M. Fazel, and P. A. Parrilo · 2010
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Concentration-based guarantees for low-rank matrix reconstruction
R. Foygel and N. Srebro · 2011
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Complexity bounds for second-order optimality in unconstrained optimization
C. Cartis, N. I. Gould, and P. L. Toint · 2012
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Approximation algorithms and semidefinite programming
B. Gärtner and J. Matousek · 2012
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Restricted strong convexity and weighted matrix completion: Optimal bounds with noise
S. Negahban and M. J. Wainwright · 2012
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A geometric analysis of phase retrieval
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Community detection and stochastic block models: recent developments
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Gradient descent can take exponential time to escape saddle points
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No spurious local minima in nonconvex low rank problems: A unified geometric analysis
R. Ge, C. Jin, and Y. Zheng · 2017
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Solving sdps for synchronization and maxcut problems via the grothendieck inequality
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Random matrices: repulsion in spectrum
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Non-square matrix sensing without spurious local minima via the burer-monteiro approach
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Sketchy decisions: Convex low-rank matrix optimization with optimal storage
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Global optimality in low-rank matrix optimization
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