Adaptive Restart for Accelerated Gradient Schemes
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A. Auslender, M. Teboulle, Interior gradient and proximal methods for convex and conic optimization, SIAM J. Optim. 16(3), 697–725 (2006).
A. Beck, M. Teboulle, A fast iterative shrinkage-thresholding algorithm for linear inverse problems, SIAM J. Imaging Sci. 2, 183–202 (2009).
S. Becker, E. Candès, M. Grant, Templates for convex cone problems with applications to sparse signal recovery, Math. Program. Comput. 3(3), 165–218 (2011).
E. Candès, J. Romberg, T. Tao, Stable signal recovery from incomplete and inaccurate measurements, Commun. Pure Appl. Math. 59(8), 1207–1223 (2006).
E. Candès, M. Wakin, An introduction to compressive sampling, IEEE Signal Process. Mag. 25(2), 21–30 (2008).
A. Chambolle, R. De Vore, N. Lee, B. Lucier, Nonlinear wavelet image processing: variational problems, compression, and noise removal through wavelet shrinkage, IEEE Trans. Image Process. 7(3), 319–335 (1998).
A. Chiang, Fundamental Methods of Mathematical Economics (McGraw-Hill, New York, 1984).
I. Daubechies, M. Defrise, C. De Mol, An iterative thresholding algorithm for linear inverse problems with a sparsity constraint, Commun. Pure Appl. Math. 57(11), 1413–1457 (2004).
M. Gu, L. Lim, C. Wu, PARNES: A rapidly convergent algorithm for accurate recovery of sparse and approximately sparse signals. Technical report (2009). arXiv:0911.0492 .
M. Hestenes, E. Stiefel, Methods of conjugate gradients for solving linear systems, J. Res. Natl. Bur. Stand. 49(6), 409–436 (1952).
G. Lan, R. Monteiro, Iteration complexity of first-order penalty methods for convex programming. Manuscript, School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, June 2008
G. Lan, Z. Lu, R. Monteiro, Primal-dual first-order methods with o(1/ϵ) iteration-complexity for cone programming, Math. Program. 1–29 (2009).
J. Liu, L. Yuan, J. Ye, An efficient algorithm for a class of fused lasso problems, in Proceedings of the 16th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, July (2010), pp. 323–332.
A. Nemirovski, Efficient methods in convex programming. Lecture notes (1994). http://www2.isye.gatech.edu/~nemirovs/Lect_EMCO.pdf .
A. Nemirovski, D. Yudin, Problem Complexity and Method Efficiency in Optimization. Wiley-Interscience Series in Discrete Mathematics (Wiley, New York, 1983).
Y. Nesterov, A method of solving a convex programming problem with convergence rate O(1/k 2), Sov. Math. Dokl. 27(2), 372–376 (1983).
Y. Nesterov, Introductory Lectures on Convex Optimization: A Basic Course (Kluwer Academic, Dordrecht, 2004).
Y. Nesterov, Gradient methods for minimizing composite objective function. CORE discussion paper (2007). http://www.ecore.be/DPs/dp_1191313936.pdf .
J. Nocedal, S. Wright, Numerical Optimization. Springer Series in Operations Research (Springer, Berlin, 2000).
B. Polyak, Introduction to Optimization. Translations Series in Mathematics and Engineering (Optimization Software, Publications Division, New York, 1987).
R. Tibshirani, Regression shrinkage and selection via the lasso, J. R. Stat. Soc. B 58(1), 267–288 (1994).
P. Tseng, On accelerated proximal gradient methods for convex-concave optimization (2008). http://pages.cs.wisc.edu/~brecht/cs726docs/Tseng.APG.pdf .