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Recent research indicates that many convex optimization problems with random constraints exhibit a phase transition as the number of constraints increases.
Tubes and spheres in n n -spaces, and a class of statistical problems
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Convex analysis and minimization algorithms. I
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On the rank minimization problem over a positive semidefinite linear matrix inequality
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Variational analysis
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Second-order cone programming
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Lectures on modern convex optimization
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Exponential bounds implying construction of compressed sensing matrices, error-correcting codes, and neighborly polytopes by random sampling
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New null space results and recovery thresholds for matrix rank minimization
S. Oymak and B. Hassibi · 2010
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NIST handbook of mathematical functions
F. W. J. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark, editors · 2010
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Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization
B. Recht, M. Fazel, and P. A. Parrilo · 2010
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Geometric analysis of the condition of the convex feasibility problem
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The concentration of measure phenomenon
M. Ledoux · 2001
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Proportional concentration phenomena on the sphere
S. Artstein · 2002
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Matrix rank minimization with applications
M. Fazel · 2002
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Complex variables: Introduction and applications
M. J. Ablowitz and A. S. Fokas · 2003
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Astronomical image representation by the curvelet transform
J.-L. Starck, D. L. Donoho, and E. J. Candès · 2003
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V. Chandrasekaran, S. Sanghavi, P. A. Parrilo, and A. S. Willsky · 2011
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Permutahedra and generalized associahedra
C. Hohlweg, C. E. M. C. Lange, and H. Thomas · 2011
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Projection volumes of hyperplane arrangements
C. J. Klivans and E. Swartz · 2011
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Analyzing weighted ℓ 1 \ell_{1} minimization for sparse recovery with nonuniform sparse models
A. Khajehnejad, W. Xu, A. S. Avestimehr, and B. Hassibi · 2011
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Improved thresholds for rank minimization
S. Oymak, M. A. Khajehnejad, and B. Hassibi · 2011
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Null space conditions and thresholds for rank minimization
B. Recht, W. Xu, and B. Hassibi · 2011
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Precise stability phase transitions for ℓ 1 \ell_{1} minimization: A unified geometric framework
W. Xu and B. Hassibi · 2011
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Intrinsic volumes of symmetric cones
D. Amelunxen and P. Bürgisser · 2012
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The LASSO risk for Gaussian matrices
M. Bayati and A. Montanari · 2012
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The convex geometry of linear inverse problems
V. Chandrasekaran, B. Recht, P. A. Parrilo, and A. S. Willsky · 2012
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Compressed sensing
Y. C. Eldar and G. Kutyniok, editors · 2012
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Anti-sparse coding for approximate nearest neighbor search
H. Jegou, T. Furon, and J.-J. Fuchs · 2012
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Fundamental thresholds in compressed sensing: a high-dimensional geometry approach
W. Xu and B. Hassibi · 2012
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Probabilistic analysis of the Grassmann condition number
D. Amelunxen and P. Bürgisser · 2013
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Universality in polytope phase transitions and message passing algorithms
M. Bayati, M. Lelarge, and A. Montanari · 2013
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Concentration inequalities: A nonasymptotic theory of independence
S. Boucheron, G. Lugosi, and P. Massart · 2013
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The phase transition of matrix recovery from Gaussian measurements matches the minimax MSE of matrix denoising
D. L. Donoho, M. Gavish, and A. Montanari · 2013
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Accurate prediction of phase transitions in compressed sensing via a connection to minimax denoising
D. L. Donoho, I. Johnstone, and A. Montanari · 2013
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A mathematical introduction to compressive sensing
S. Foucart and H. Rauhut · 2013
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A geometric analysis of convex demixing
M. B. McCoy · 2013
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Square deal: Lower bounds and improved relaxations for tensor recovery
C. Mu, B. Huang, J. Wright, and D. Goldfarb · 2013
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The achievable performance of convex demixing
M. B. McCoy and J. A. Tropp · 2013
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Sharp MSE bounds for proximal denoising
S. Oymak and B. Hassibi · 2013
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M. Stojnic · 2013
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Corrupted sensing: Novel guarantees for separating structured signals
R. Foygel and L. Mackey · 2014
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Snowmaker: Matlab code for statistical dimension computations
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From Steiner formulas for cones to concentration of intrinsic volumes
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Sharp recovery bounds for convex demixing, with applications
M. B. McCoy and J. A. Tropp · 2014
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