@article {vandenberg2011SIAMsol,
	title = {Sparse optimization with least-squares constraints},
	journal = {SIAM Journal on Optimization},
	volume = {21},
	number = {4},
	year = {2011},
	month = {11},
	pages = {1201{\textendash}1229},
	abstract = {The use of convex optimization for the recovery of sparse signals from incomplete or compressed data is now common practice. Motivated by the success of basis pursuit in recovering sparse vectors, new formulations have been proposed that take advantage of different types of sparsity. In this paper we propose an efficient algorithm for solving a general class of sparsifying formulations. For several common types of sparsity we provide applications, along with details on how to apply the algorithm, and experimental results.},
	keywords = {basis pursuit, compressed sensing, convex program, duality, group sparsity, matrix completion, Newton{\textquoteright}s method, root-finding, sparse solutions},
	doi = {10.1137/100785028},
	url = {http://www.math.ucdavis.edu/\%7Empf/2010-sparse-optimization-with-least-squares.html},
	author = {Ewout van den Berg and Michael P. Friedlander}
}
@article {berg2008SJSCpareto,
	title = {Probing the Pareto frontier for basis pursuit solutions},
	journal = {SIAM Journal on Scientific Computing},
	volume = {31},
	number = {2},
	year = {2008},
	month = {01},
	pages = {890-912},
	publisher = {SIAM},
	abstract = {The basis pursuit problem seeks a minimum one-norm solution of an underdetermined least-squares problem. Basis pursuit denoise (BPDN) fits the least-squares problem only approximately, and a single parameter determines a curve that traces the optimal trade-off between the least-squares fit and the one-norm of the solution. We prove that this curve is convex and continuously differentiable over all points of interest, and show that it gives an explicit relationship to two other optimization problems closely related to BPDN. We describe a root-finding algorithm for finding arbitrary points on this curve; the algorithm is suitable for problems that are large scale and for those that are in the complex domain. At each iteration, a spectral gradient-projection method approximately minimizes a least-squares problem with an explicit one-norm constraint. Only matrix-vector operations are required. The primal-dual solution of this problem gives function and derivative information needed for the root-finding method. Numerical experiments on a comprehensive set of test problems demonstrate that the method scales well to large problems.},
	keywords = {basis pursuit, convex program, duality, Newton{\textquoteright}s method, one-norm regularization, Optimization, projected gradient, root-finding, sparse solutions},
	doi = {10.1137/080714488},
	url = {https://slim.gatech.edu/Publications/Public/Journals/SIAMJournalOnScientificComputing/2008/vanderberg08SIAMptp/vanderberg08SIAMptp.pdf},
	author = {Ewout van den Berg and Michael P. Friedlander}
}
