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Most learning methods with rank or sparsity constraints use convex relaxations, which lead to optimization with the nuclear norm or the $\ell_1$-norm.
Symmetric gauge functions and unitarily invariant norms
Mirsky, L · 1960
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On estimation of a probability density function and mode
Parzen, E · 1962
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Integer and combinatorial optimization , volume 18
Nemhauser, G.L. and Wolsey, L.A · 1988
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Least squares mixture decomposition estimation
Kim, D · 1995
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Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information
Candès, E., Romberg, J., and Tao, T · 2006
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Probing the Pareto frontier for basis pursuit solutions
van den Berg, E. and Friedlander, M. P · 2008
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Sparse and stable Markowitz portfolios
Brodie, J., Daubechies, I., De Mol, C., Giannone, D., and Loris, I · 2009
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A generalized approach to portfolio optimization: Improving performance by constraining portfolio norms
DeMiguel, V., Garlappi, L., Nogales, F.J., and Uppal, R · 2009
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Gradient descent with sparsification: an iterative algorithm for sparse recovery with restricted isometry property
Garg, R. and Khandekar, R · 2009
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SPADES and mixture models
Bunea, F., Tsybakov, A.B., Wegkamp, M.H., and Barbu, A · 2010
Cited alongside, same era.
Sparse recovery algorithms: sufficient conditions in terms of restricted isometry constants
Foucart, S · 2010
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Quantum state tomography via compressed sensing
Gross, D., Liu, Y.-K., Flammia, S. T., Becker, S., and Eisert, J · 2010
Cited alongside, same era.
Guaranteed rank minimization via singular value projection
Meka, Raghu, Jain, Prateek, and Dhillon, Inderjit S · 2010
Templates for convex cone problems with applications to sparse signal recovery
Becker, Stephen, Candès, Emmanuel, and Grant, Michael · 2011
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Recipes on hard thresholding methods
Kyrillidis, A. and Cevher, V · 2011
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Universal low-rank matrix recovery from Pauli measurements
Liu, Y.K · 2011
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Quantum tomography via compressed sensing: error bounds, sample complexity and efficient estimators
Flammia, S.T., Gross, D., Liu, Y.K., and Eisert, J · 2012
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Combinatorial selection and least absolute shrinkage via the Clash
Kyrillidis, A. and Cevher, V · 2012
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Recovery of sparse probability measures via convex programming
Pilanci, M., El Ghaoui, L., and Chandrasekaran, V · 2012
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Cited alongside, same era.
Greedy sparsity-constrained optimization
Bahmani, S., Boufounos, P., and Raj, B · 2011
Cited alongside, same era.