@presentation {pong2013SINBADppg,
	title = {The proximal-proximal gradient algorithm},
	year = {2013},
	publisher = {SINBAD},
	abstract = {In many applications, one has to minimize the sum of a smooth loss function modeling misfit and a regularization term inducing structures. In this talk, we consider the case when the regularization is a composition of a convex function, whose proximal mapping is easy to compute, and a nonzero linear map. Such instances arise in system identification and realization problems. In this talk, we present a new algorithm, the proximal-proximal gradient algorithm, which admits easy subproblems. Our algorithm reduces to the proximal gradient algorithm if the linear map is just the identity map, and can be viewed as "very inexact" inexact proximal gradient algorithm. We show that the whole sequence generated from the algorithm converges to an optimal solution, and establish an upper bound on iteration complexity.},
	keywords = {Presentation, SINBAD, SINBADFALL2013, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2013/Fall/pong2013SINBADppg/pong2013SINBADppg.pdf},
	author = {Ting Kei Pong and Michael P. Friedlander and Felix J. Herrmann}
}
@presentation {nutini2013SINBADpcb,
	title = {Putting the curvature back into sparse solvers},
	year = {2013},
	publisher = {SINBAD},
	abstract = {For many problems in signal and image processing, we seek a sparse solution that solves that approximately solves the problem Ax $\approx$ b, where A is an m-by-n matrix and b is an m-vector. Many of the most used approaches to problem thissuch as iterative soft thresholding SPGL1 andare first-order methods. As a result, these methods can sometimes be slow to converge. In this talk, we present an approach that takes advantage of the easily-obtainable second-order information. By exploiting this available second-order information, we are able to put the curvature back into sparse solvers and improve upon the convergence rates of existing solvers.},
	keywords = {Presentation, SINBAD, SINBADFALL2013, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2013/Fall/nutini2013SINBADpcb/nutini2013SINBADpcb.pdf},
	author = {Julie Nutini and Michael P. Friedlander and Felix J. Herrmann}
}
@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}
}
