Open Access
Issue
ESAIM: COCV
Volume 26, 2020
Article Number 28
Number of page(s) 20
DOI https://doi.org/10.1051/cocv/2019011
Published online 18 March 2020
  1. H. Attouch and J. Bolte, On the convergence of the proximal algorithm for nonsmooth functions involving analytic features. Math. Program. Ser. B 116 (2009) 5–16. [CrossRef] [MathSciNet] [Google Scholar]
  2. H. Attouch, J. Bolte and B.F. Svaiter, Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward-backward splitting, and regularized Gauss-Seidel methods. Math. Program. 137 (2013) 91–129. [Google Scholar]
  3. A. Barbara, A. Jourani and S. Vaiter, Maximal Solutions of Sparse Analysis Regularization. Preprint arXiv:1703.00192 (2017). [Google Scholar]
  4. H.H. Bauschke and P. Combettes, Convex Analysis and Monotone Operator Theory, CMS Books in Mathematics, 2nd edn. Springer, Berlin (2017). [CrossRef] [Google Scholar]
  5. A. Blanchet and J. Bolte, A family of functional inequalities: Lojasiewicz inequalities and displacement convex functions. J. Funct. Anal. 275 (2018) 1650–1673. [Google Scholar]
  6. J. Bolte, T.-P. Nguyen, J. Peypouquet and B. Suter, From error bounds to the complexity of first-order descent methods for convex functions. Math. Programm. 165 (2017) 471–507. [CrossRef] [Google Scholar]
  7. J.M. Borwein and A. Lewis, Partially finite convex programming, part I: Quasi relative interiors and duality theory. Math. Programm. 57 (1992) 15–48. [CrossRef] [Google Scholar]
  8. K. Bredies and D.A. Lorenz, Linear convergence of iterative soft-thresholding. J. Fourier Anal. Appl. 14 (2008) 813–837. [Google Scholar]
  9. P.L. Combettes and J.-C. Pesquet, Proximal thresholding algorithm for minimization over orthonormal bases. SIAM J. Optim. 18 (2007) 1351–1376. [Google Scholar]
  10. P.L. Combettes, S. Salzo and S. Villa, Consistency of regularized learning schemes in Banach spaces. Math. Programm. published online 2017-03-25. [Google Scholar]
  11. I. Daubechies, M. Defrise and C. De Mol, An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Commun. Pure Appl. Math. 57 (2004) 1413–1457. [Google Scholar]
  12. D. Davis and W. Yin, Convergence rate analysis of several splitting schemes, in Splitting Methods in Communication, Imaging, Science, and Engineering. Springer International Publishing, Switzerland (2016) 115–163. [CrossRef] [Google Scholar]
  13. C. De Mol, E. De Vito and L. Rosasco, Elastic-net regularization in learning theory. J. Complexity 25 (2009) 201–230. [CrossRef] [Google Scholar]
  14. K. Degraux, G. Peyré, J. Fadili and L. Jacques, Sparse support recovery with non-smooth loss functions, in Advances in Neural Information Processing Systems (2016) 4269–4277. [Google Scholar]
  15. C. Dossal, A necessary and sufficient condition for exact recovery by l1 minimization. Comptes Rendus Mathématique 350 (2011) 117–120. [CrossRef] [Google Scholar]
  16. D. Drusvyatskiy and A.D. Lewis, Error bounds, quadratic growth, and linear convergence of proximal methods. Math. Oper. Res. (2018) published online. [Google Scholar]
  17. V. Duval and G. Peyré, Sparse spikes super-resolution on thin grids I: the LASSO. Inverse Probl. 33 (2017) 055008. [Google Scholar]
  18. J. Fadili, J. Malick and G. Peyré, Sensitivity analysis for Mirror-Stratifiable convex functions. Preprint arXiv:1707.03194 (2017). [Google Scholar]
  19. P. Frankel, G. Garrigos and J. Peypouquet, Splitting methods with variable metric for Kurdyka-Łojasiewicz functions and general convergence rates. J. Optim. Theory Appl. 165 (2015) 874–900. [Google Scholar]
  20. G. Garrigos, L. Rosasco and S. Villa, Convergence of the Forward-Backward algorithm: beyond the worst case with the help of geometry. Preprint arXiv:1703.09477 (2017). [Google Scholar]
  21. E.T. Hale, W. Yin and Y. Zhang, Fixed-point continuation for 1-minimization: methodology and convergence. SIAM J. Optim. 19 (2008) 1107–1130. [Google Scholar]
  22. W.L. Hare and A.S. Lewis, Identifying active constraints via partial smoothness and prox-regularity. J. Convex Anal. 11 (2004) 251–266. [Google Scholar]
  23. J.-B. Hiriart-Urruty and C. Lemaréchal, Convex Analysis and Minimization Algorithms I: Fundamentals. Springer Science & Business Media, Berlin (1993). [CrossRef] [Google Scholar]
  24. B. Lemaire, Stability of the iteration method for non expansive mappings. Serdica Math. J. 22 (1996) 331–340. [Google Scholar]
  25. G. Li, Global error bounds for piecewise convex polynomials. Math. Programm. 137 (2013) 37–64. [CrossRef] [Google Scholar]
  26. J. Liang, J. Fadili and G. Peyré, Local linear convergence of Forward–Backward under partial smoothness, in Advances in Neural Information Processing Systems (2014) 1970–1978. [Google Scholar]
  27. J. Liang, J. Fadili and G. Peyré, Activity identification and local linear convergence of Forward-Backward-type methods. SIAM J. Optim. 27 (2017) 408–437. [Google Scholar]
  28. S. Mosci, L. Rosasco, M. Santoro, A. Verri and S. Villa, Solving structured sparsity regularization with proximal methods, in Machine Learning and Knowledge Discovery in Databases, edited by J.L. Balcázar, F. Bonchi, A. Gionis, M. Sebag, ECML PKDD 2010. Vol 6322 of Lecture Notes in Computer Science. Springer, Berlin, Heidelberg (2010). [Google Scholar]
  29. I. Necoara, Y. Nesterov and F. Glineur, Linear convergence of first order methods for non-strongly convex optimization. Math. Programm. 175 (2018) 69–107. [CrossRef] [Google Scholar]
  30. J. Nutini, M. Schmidt and W. Hare, “Active-set complexity” of proximal gradient: how long does it take to find the sparsity pattern?. Preprint arXiv:1712.03577 (2017). [Google Scholar]
  31. J. Peypouquet, Convex Optimization in Normed Spaces: Theory, Methods and Examples. Springer Science & Buisness Media, Switzerland (2015). [Google Scholar]
  32. J. Peypouquet and S. Sorin, Evolution equations for maximal monotone operators: asymptotic analysis in continuous and discrete time. J. Convex Anal. 17 (2010) 1113–1163. [Google Scholar]
  33. R.T. Rockafellar, Convex Analysis, Vol. 28 of Princeton Mathematical Series. Princeton University Press, Princeton, NJ (1970). [Google Scholar]
  34. C. Zalinescu, Convex Analysis in General Vector Spaces. World Scientific, NJ (2002). [CrossRef] [Google Scholar]
  35. H. Zou and T. Hastie, Regularization and variable selection via the elastic net. J. R. Stat. Soc. Ser. B 67 (2005) 301–320. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.