@presentation {macedo2013SINBADdap,
	title = {A dual approach to PhaseLift via gauge programming and bundle methods},
	year = {2013},
	publisher = {SINBAD},
	abstract = {A feature common to many sparse optimization problems is that the number of variables may be significantly larger than the number of constraints- e.g., the matrix-lifting approach taken by PhaseLift for phase retrieval results in a problem where the number of variables is quadratic in the number of constraints. We consider a duality framework and numerical methods to leverage the relatively small number of constraints. Preliminary numerical results illustrate our approach and its flexibility.},
	keywords = {Presentation, SINBAD, SINBADFALL2013, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2013/Fall/macedo2013SINBADdap/macedo2013SINBADdap.pdf},
	author = {Ives Macedo and Michael P. Friedlander and Felix J. Herrmann}
}
@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}
}
@presentation {goh2013SINBADttt,
	title = {Taming time through tangents},
	year = {2013},
	publisher = {SINBAD},
	abstract = {Given two vectors of (possibly) different lengths, the edit distance considers all possible alignments between the two and picks the one that minimizes the number of operations needed to turn one into the other. Though highly non-smooth and riddled with local minima, we show a way to compute the convex envelope of this function, which opens the door to using the approximate edit distance as a surrogate for the L2 distance and comparing vectors of different lengths.},
	keywords = {Presentation, SINBAD, SINBADFALL2013, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2013/Fall/goh2013SINBADttt/goh2013SINBADttt.pdf},
	author = {Gabriel Goh and Michael P. Friedlander and Felix J. Herrmann}
}
@presentation {friedlander2012SINBADrsh,
	title = {Randomized sampling: How confident are you?},
	year = {2012},
	publisher = {SINBAD},
	abstract = {At last year{\textquoteright}s consortium meeting, I described an inexact gradient method and sampling scheme for data fitting. The randomization method has good convergence properties, at least as measured by the distance to the solution{\textendash}{\textendash}in expectation. But as one insightful critic rightly pointed out, we don{\textquoteright}t usually observe the expectation, at least not in a single run. In this talk I will characterize the convergence of the method in terms of bounds on the probability of being too far away from the solution.},
	keywords = {Presentation, SINBAD, SINBADFALL2012, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2012/Fall/friedlander2012SINBADrsh/friedlander2012SINBADrsh_pres.pdf},
	author = {Michael P. Friedlander}
}
@presentation {friedlander2011SINBADrir,
	title = {Robust inversion, data-fitting, and inexact gradient methods},
	year = {2011},
	publisher = {SINBAD},
	keywords = {Presentation, SINBAD, SINBADFALL2011, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2011/Fall/friedlander2011SINBADrir/friedlander2011SINBADrir_pres.pdf},
	author = {Michael P. Friedlander}
}
@presentation {friedlander2010SINBADaso,
	title = {Algorithms for sparse optimization},
	year = {2010},
	publisher = {SINBAD},
	keywords = {Presentation, SINBAD, SINBADFALL2010, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2010/Fall/friedlander2010SINBADaso/friedlander2010SINBADaso_pres.pdf},
	author = {Michael P. Friedlander}
}
@presentation {friedlander2010SINBADisl,
	title = {Introduction to Spot: a linear-operator toolbox},
	year = {2010},
	publisher = {SINBAD},
	keywords = {Presentation, SINBAD, SINBADFALL2010, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2010/Fall/friedlander2010SINBADisl/friedlander2010SINBADisl_pres.pdf},
	author = {Michael P. Friedlander}
}
@conference {friedlander2009NUalssr,
	title = {Algorithms for large-scale sparse reconstruction},
	booktitle = {IEMS},
	year = {2009},
	publisher = {IEMS Colloquim Speaker},
	organization = {IEMS Colloquim Speaker},
	address = {Northwestern University},
	keywords = {minimization, SLIM},
	author = {Michael P. Friedlander}
}
@conference {friedlander2009VIETcsgpa,
	title = {Computing sparse and group-sparse approximations},
	booktitle = {VIET},
	year = {2009},
	publisher = {2009 High Performance Scientific Computing Conference},
	organization = {2009 High Performance Scientific Computing Conference},
	address = {Hanoi, Vietnam},
	keywords = {minimization, SLIM},
	author = {Michael P. Friedlander}
}
@conference {vandenberg2009SLIMocf,
	title = {Optimizing costly functions with simple constraints: a limited-memory projected Quasi-Newton algorithm},
	booktitle = {SLIM},
	series = {Twelfth International Conference on Artificial Intelligence and Statistics},
	volume = {12},
	year = {2009},
	month = {04},
	abstract = {An optimization algorithm for minimizing a smooth function over a convex set is described. Each iteration of the method computes a descent direction by minimizing, over the original constraints, a diagonal-plus low-rank quadratic approximation to the function. The quadratic approximation is constructed using a limited-memory quasi-Newton update. The method is suitable for large-scale problems where evaluation of the function is substan- tially more expensive than projection onto the constraint set. Numerical experiments on one-norm regularized test problems indicate that the proposed method is competitve with state-of-the-art methods such as bound-constrained L-BFGS and orthant-wise descent. We further show that the method generalizes to a wide class of problems, and substantially improves on state-of-the-art methods for problems such as learning the structure of Gaussian graphi- cal models (involving positive-definite matrix constraints) and Markov random fields (involving second-order cone constraints).},
	keywords = {SLIM},
	url = {http://www.cs.ubc.ca/ mpf/papers/SchmidtBergFriedMurph09.pdf},
	author = {Ewout van den Berg and Mark Schmidt and Michael P. Friedlander and K. Murphy}
}
@conference {friedlander2009SCAIMspot,
	title = {Spot: A linear-operator toolbox for Matlab},
	booktitle = {SCAIM},
	year = {2009},
	publisher = {SCAIM Seminar},
	organization = {SCAIM Seminar},
	address = {University of British Columbia},
	keywords = {minimization, Presentation, SLIM},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2009/VandenBerg-Mon-1130.pdf},
	author = {Ewout van den Berg and Michael P. Friedlander}
}
@conference {friedlander2008SIAMasa,
	title = {Active-set approaches to basis pursuit denoising},
	booktitle = {SIAM Optimization},
	year = {2008},
	month = {05},
	publisher = {SIAM Optimization},
	organization = {SIAM Optimization},
	keywords = {SLIM},
	url = {http://www.cs.ubc.ca/ mpf/public/mpf08siopt.pdf},
	author = {Michael P. Friedlander}
}
@conference {friedlander2008SINBADafl,
	title = {Algorithms for large-scale sparse reconstruction},
	booktitle = {SINBAD 2008},
	year = {2008},
	abstract = {Many signal processing applications seek to approximate a signal as a linear combination of only a few elementary atoms drawn from a large collection. This is known as sparse reconstruction, and the theory of compressed sensing allows us to pose it as a structured convex optimization problem. I will discuss the role of duality in revealing some unexpected and useful properties of these problems, and will show how they can lead to practical, large-scale algorithms. I will also describe some applications of these algorithms.},
	keywords = {SINBAD, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2008/friedlander2008SINBADafl/friedlander2008SINBADafl.pdf},
	author = {Michael P. Friedlander}
}
@techreport {vandenberg08gsv,
	title = {Group sparsity via linear-time projection},
	number = {TR-2008-09},
	year = {2008},
	month = {06},
	institution = {UBC - Department of Computer Science},
	abstract = {We present an efficient spectral projected-gradient algorithm for optimization subject to a group one-norm constraint. Our approach is based on a novel linear-time algorithm for Euclidean projection onto the one- and group one-norm constraints. Numerical experiments on large data sets suggest that the proposed method is substantially more efficient and scalable than existing methods.},
	keywords = {Optimization, SLIM},
	url = {http://www.optimization-online.org/DB_FILE/2008/07/2056.pdf},
	author = {Ewout van den Berg and Mark Schmidt and Michael P. Friedlander and K. Murphy}
}
@article {hennenfent2008GEOPnii,
	title = {New insights into one-norm solvers from the Pareto curve},
	journal = {Geophysics},
	volume = {73},
	number = {4},
	year = {2008},
	month = {07},
	pages = {A23-A26},
	abstract = {Geophysical inverse problems typically involve a trade off between data misfit and some prior. Pareto curves trace the optimal trade off between these two competing aims. These curves are commonly used in problems with two-norm priors where they are plotted on a log-log scale and are known as L-curves. For other priors, such as the sparsity-promoting one norm, Pareto curves remain relatively unexplored. We show how these curves lead to new insights in one-norm regularization. First, we confirm the theoretical properties of smoothness and convexity of these curves from a stylized and a geophysical example. Second, we exploit these crucial properties to approximate the Pareto curve for a large-scale problem. Third, we show how Pareto curves provide an objective criterion to gauge how different one-norm solvers advance towards the solution.},
	keywords = {Acquisition, Geophysics, Optimization, Pareto, Processing, SLIM},
	doi = {10.1190/1.2944169},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2008/hennenfent08GEOnii/hennenfent08GEOnii.pdf},
	author = {Gilles Hennenfent and Ewout van den Berg and Michael P. Friedlander and Felix J. Herrmann}
}
@article {friedlander2007TASdtd,
	title = {Discussion: the Dantzig selector: statistical estimation when p is much larger than n},
	journal = {The Annals of Statistics},
	volume = {35},
	number = {6},
	year = {2007},
	month = {03},
	pages = {2385-2391},
	keywords = {dantzig, SLIM, statistics},
	doi = {10.1214/009053607000000479},
	author = {Michael P. Friedlander and M. A. Saunders}
}
@article {friedlander2007SJOero,
	title = {Exact regularization of convex programs},
	journal = {SIAM Journal on Optimization},
	volume = {18},
	number = {4},
	year = {2007},
	month = {05},
	pages = {1326-1350},
	abstract = {The regularization of a convex program is exact if all solutions of the regularized problem are also solutions of the original problem for all values of the regularization parameter below some positive threshold. For a general convex program, we show that the regularization is exact if and only if a certain selection problem has a Lagrange multiplier. Moreover, the regularization parameter threshold is inversely related to the Lagrange multiplier. We use this result to generalize an exact regularization result of Ferris and Mangasarian [Appl. Math. Optim., 23(1991), pp. 266{\textendash}273] involving a linearized selection problem. We also use it to derive necessary and sufficient conditions for exact penalization, similar to those obtained by Bertsekas [Math. Programming, 9(1975), pp. 87{\textendash}99] and by Bertsekas, Nedi , Ozdaglar [Convex Analysis and Optimization, Athena Scientific, Belmont, MA, 2003]. When the regularization is not exact, we derive error bounds on the distance from the regularized solution to the original solution set. We also show that existence of a {\textquoteleft}{\textquoteleft}weak sharp minimum{\textquoteright}{\textquoteright} is in some sense close to being necessary for exact regularization. We illustrate the main result with numerical experiments on the l1 regularization of benchmark (degenerate) linear programs and semidefinite/second-order cone programs. The experiments demonstrate the usefulness of l1 regularization in finding sparse solutions.},
	keywords = {Optimization, SLIM},
	doi = {10.1137/060675320},
	author = {Michael P. Friedlander and P. Tseng}
}
@conference {vandenberg2007SINBADipo1,
	title = {In pursuit of a root},
	booktitle = {2007 Von Neumann Symposium},
	year = {2007},
	keywords = {minimization, Presentation, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2007/vandenberg2007SINBADipo1/vandenberg2007SINBADipo1.pdf},
	author = {Ewout van den Berg and Michael P. Friedlander}
}
@manual {vandenberg07MNsat,
	title = {SPARCO: a toolbox for testing sparse reconstruction algorithms},
	year = {2007},
	month = {10},
	abstract = {Sparco is a suite of problems for testing and benchmarking algorithms for sparse signal reconstruction. It is also an environment for creating new test problems, and a suite of standard linear operators is provided from which new problems can be assembled. Sparco is implement ed entirely in Matlab and is self contained. (A few optional test problems are based on the CurveLab toolbox, which can be installed separately.) At the core of the sparse recovery problem is the linear system $Ax+r=b$, where $A$ is an $m$-by-$n$ linear operator and the $m$-vector $b$ is the observed signal. The goal is to find a sparse $n$-vector $x$ such that $r$ is small in norm.},
	keywords = {SLIM},
	url = {http://www.cs.ubc.ca/labs/scl/sparco/},
	author = {Ewout van den Berg and Michael P. Friedlander}
}
