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Backtracking line-search is an old yet powerful strategy for finding a better step sizes to be used in proximal gradient algorithms.
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The Łojasiewicz inequality for nonsmooth subanalytic functions with applications to subgradient dynamical systems
J. Bolte, A. Daniilidis, and A. Lewis · 2006
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Clarke subgradients of stratifiable functions
J. Bolte, A. Daniilidis, A.S. Lewis, and M. Shiota · 2007
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Enhancing sparsity by reweighted ℓ 1 \ell_{1} minimization
E. J. Candes, M. B. Wakin, and S. Boyd · 2008
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On the convergence of the proximal algorithm for nonsmooth functions involving analytic features
H. Attouch and J. Bolte · 2009
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A fast iterative shrinkage-thresholding algorithm for linear inverse problems
A. Beck and M. Teboulle · 2009
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Proximal alternating minimization and projection methods for nonconvex problems: an approach based on the Kurdyka-Łojasiewicz inequality
Inertial proximal alternating linearized minimization (iPALM) for nonconvex and nonsmooth problems
T. Pock and S. Sabach · 2016
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A descent lemma beyond Lipschitz gradient continuity: first-order methods revisited and applications
H. H. Bauschke, J. Bolte, and M. Teboulle · 2017
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Solving (most) of a set of quadratic equalities: Composite optimization for robust phase retrieval
J.C. Duchi and F. Ruan · 2017
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Phase retrieval, What’s new?
D. R. Luke · 2017
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Linear convergence of proximal gradient algorithm with extrapolation for a class of nonconvex nonsmooth minimization problems
B. Wen, X. Chen, and T. K. Pong · 2017
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H. Attouch, J. Bolte, P. Redont, and A. Soubeyran · 2010
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Characterizations of Łojasiewicz inequalities: subgradient flows, talweg, convexity
J. Bolte, A. Daniilidis, O. Ley, and L. Mazet · 2010
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Fundamentals of Convex Analysis
J.-B. Hiriart-Urruty and C. Lemarechal · 2012
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Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward–backward splitting, and regularized Gauss–Seidel methods
H. Attouch, J. Bolte, and B. F. Svaiter · 2013
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A general iterative shrinkage and thresholding algorithm for non-convex regularized optimization problems
P. Gong, C. Zhang, L. Zhaosong, J. Z. Huang, and J. Ye · 2013
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Proximal alternating linearized minimization for nonconvex and nonsmooth problems
J. Bolte, S. Sabach, and M. Teboulle · 2014
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iPiano: inertial proximal algorithm for nonconvex optimization
P. Ochs, Y. Chen, T. Brox, and T. Pock · 2014
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First order methods beyond convexity and Lipschitz gradient continuity with applications to quadratic inverse problems
J. Bolte, S. Sabach, M. Teboulle, and Y. Vaisbourd · 2018
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Variational phase retrieval with globally convergent preconditioned proximal algorithm
H. Chang, S. Marchesini, Y. Lou, and T. Zeng · 2018
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Local convergence of the heavy-ball method and ipiano for non-convex optimization
P. Ochs · 2018
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A simplified view of first order methods for optimization
M. Teboulle · 2018
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Solving systems of random quadratic equations via truncated amplitude flow
G. Wang, G. B. Giannakis, and Y. C. Eldar · 2018
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M. C. Mukkamala and P. Ochs · 2019
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Bregman proximal framework for deep linear neural networks, 2019
M. C. Mukkamala, F. Westerkamp, E. Laude, D. Cremers, and P. Ochs · 2019
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Unifying abstract inexact convergence theorems and block coordinate variable metric ipiano
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