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We show that several classical quantities controlling compressed sensing performance directly match classical parameters controlling algorithmic complexity.
Rockafellar, R. T. [1970],
1970
Earlier work this paper cites.
Nesterov, Y. [1983], ‘A method of solving a convex programming problem with convergence rate
1983
Earlier work this paper cites.
Corrected reprint of the 1985 original
Horn, R. A. and Johnson, C. R. [1990], · 1985
Earlier work this paper cites.
Nemirovskii, A. and Nesterov, Y. E. [1985], ‘Optimal methods of smooth convex minimization’,
1985
Earlier work this paper cites.
Pajor, A. and Tomczak-Jaegermann, N. [1986], ‘Subspaces of small codimension of finite-dimensional banach spaces’,
1986
Earlier work this paper cites.
Renegar, J. [1995
1995
Earlier work this paper cites.
Renegar, J. [1995
1995
Earlier work this paper cites.
Tibshirani, R. [1996], ‘Regression shrinkage and selection via the LASSO’,
1996
Earlier work this paper cites.
Freund, R. M. and Vera, J. R. [1999
1999
Earlier work this paper cites.
Freund, R. M. and Vera, J. R. [1999
1999
Earlier work this paper cites.
Epelman, M. and Freund, R. M. [2000], ‘Condition number complexity of an elementary algorithm for computing a reliable solution of a conic linear system’,
2000
Earlier work this paper cites.
Peña, J. [2000], ‘Understanding the geometry of infeasible perturbations of a conic linear system’,
2000
Earlier work this paper cites.
Donoho, D. and Huo, X. [2001], ‘Uncertainty principles and ideal atomic decomposition’,
2001
Earlier work this paper cites.
Grant, M., Boyd, S. and Ye, Y. [2001], ‘CVX: Matlab software for disciplined convex programming’
2001
Earlier work this paper cites.
Renegar, J. [2001],
2001
Earlier work this paper cites.
Feuer, A. and Nemirovski, A. [2003], ‘On sparse representation in pairs of bases’,
2003
Earlier work this paper cites.
Freund, R. M. and Vera, J. R. [2003], ‘On the complexity of computing estimates of condition measures of a conic linear system’,
2003
Earlier work this paper cites.
Ordóñez, F. and Freund, R. M. [2003], ‘Computational experience and the explanatory value of condition measures for linear optimization’,
2003
Earlier work this paper cites.
Boyd, S. and Vandenberghe, L. [2004],
2004
Earlier work this paper cites.
Efron, B., Hastie, T., Johnstone, I. and Tibshirani, R. [2004], ‘Least angle regression’,
2004
Earlier work this paper cites.
Donoho, D. L. and Tanner, J. [2005], ‘Sparse nonnegative solutions of underdetermined linear equations by linear programming’,
2005
Earlier work this paper cites.
Nesterov, Y. [2005], ‘Smooth minimization of non-smooth functions’,
2005
Cited alongside, same era.
Candes, E. J., Romberg, J. K. and Tao, T. [2006], ‘Stable signal recovery from incomplete and inaccurate measurements’,
2006
Cited alongside, same era.
Candès, E. and Tao, T. [2006], ‘Near-optimal signal recovery from random projections: Universal encoding strategies?’,
2006
Cited alongside, same era.
Bolte, J., Daniilidis, A. and Lewis, A. [2007], ‘The lojasiewicz inequality for nonsmooth subanalytic functions with applications to subgradient dynamical systems’,
2007
Cited alongside, same era.
Kashin, B. and Temlyakov, V. [2007], ‘A remark on compressed sensing’,
2007
Cited alongside, same era.
2011
Later among the works it cites.
Vershynin, R. [2011],
2011
Later among the works it cites.
Chandrasekaran, V., Recht, B., Parrilo, P. and Willsky, A. [2012], ‘The convex geometry of linear inverse problems’,
2012
Later among the works it cites.
Chandrasekaran, V. and Jordan, M. I. [2013], ‘Computational and statistical tradeoffs via convex relaxation’,
2013
Later among the works it cites.
Luss, R. and Teboulle, M. [2013], ‘Conditional gradient algorithmsfor rank-one matrix approximations with a sparsity constraint’,
2013
Later among the works it cites.
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2007
Cited alongside, same era.
Donoho, D. L. and Tsaig, Y. [2008], ‘Fast solution of
2008
Cited alongside, same era.
2008
Cited alongside, same era.
Recht, B., Xu, W. and Hassibi, B. [2008], Necessary and sufficient conditions for success of the nuclear norm heuristic for rank minimization,
2008
Cited alongside, same era.
Beck, A. and Teboulle, M. [2009], ‘A fast iterative shrinkage-thresholding algorithm for linear inverse problems’,
2009
Cited alongside, same era.
Belloni, A. and Freund, R. M. [2009], ‘A geometric analysis of renegar’s condition number, and its interplay with conic curvature’,
2009
Cited alongside, same era.
Belloni, A., Freund, R. M. and Vempala, S. [2009], ‘An efficient rescaled perceptron algorithm for conic systems’,
2009
Cited alongside, same era.
2014
Later among the works it cites.
Amelunxen, D., Lotz, M., McCoy, M. B. and Tropp, J. A. [2014], ‘Living on the edge: Phase transitions in convex programs with random data’,
2014
Later among the works it cites.
Asif, M. S. and Romberg, J. [2014], ‘Sparse recovery of streaming signals using l1-homotopy’,
2014
Later among the works it cites.
Boumal, N., Mishra, B., Absil, P.-A. and Sepulchre, R. [2014], ‘Manopt, a Matlab toolbox for optimization on manifolds’,
2014
Later among the works it cites.
Deshpande, Y., Montanari, A. and Richard, E. [2014], Cone-constrained principal component analysis,
2014
Later among the works it cites.
Giselsson, P. and Boyd, S. [2014], Monotonicity and restart in fast gradient methods,
2014
Later among the works it cites.
Juditsky, A., Karzan, F. K. and Nemirovski, A. [2014], ‘On a unified view of nullspace-type conditions for recoveries associated with general sparsity structures’,
2014
Later among the works it cites.
Su, W., Boyd, S. and Candes, E. [2014], A differential equation for modeling nesterov’s accelerated gradient method: Theory and insights,
2014
Later among the works it cites.
Yen, I. E.-H., Hsieh, C.-J., Ravikumar, P. K. and Dhillon, I. S. [2014], Constant nullspace strong convexity and fast convergence of proximal methods under high-dimensional settings,
2014
Later among the works it cites.
O’Donoghue, B. and Candes, E. [2015], ‘Adaptive restart for accelerated gradient schemes’,
2015
Closest in time.
2015
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Boumal, N. [2016], ‘Nonconvex phase synchronization’,
2016
Closest in time.
2016
Closest in time.
Roulet, V. and d’Aspremont, A. [2017], ‘Sharpness, restart and acceleration’,
2017
Closest in time.
Zhong, Y. and Boumal, N. [2017], ‘Near-optimal bounds for phase synchronization’,
2017
Closest in time.
Zhou, Z. and So, A. M.-C. [2017], ‘A unified approach to error bounds for structured convex optimization problems’,
2017
Closest in time.