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In many modern machine learning applications, structures of underlying mathematical models often yield nonconvex optimization problems.
Ensembles semi-analytiques
Łojasiewicz, S · 1965
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A method of solving a convex programming problem with convergence rate O ( 1 / k 2 ) O(1/k^{2})
Nesterov, Y · 1983
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Variational Analysis
Rockafellar, R.T. and Wets, R.J.B · 1997
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On gradients of functions definable in o-minimal structures
Kurdyka, K · 1998
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The Łojasiewicz inequality for nonsmooth subanalytic functions with applications to subgradient dynamical systems
Bolte, J., Daniilidis, A., and Lewis, A · 2007
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On the convergence of the proximal algorithm for nonsmooth functions involving analytic features
Attouch, H. and Bolte, J · 2009
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Proximal alternating minimization and projection methods for nonconvex problems: An approach based on the Kurdyka-Łojasiewicz inequality
Attouch, H., Bolte, J., Redont, P., and Soubeyran, A · 2010
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Characterizations of Łojasiewicz inequalities and applications: Subgradient flows, talweg, convexity
Bolte, J., Danilidis, A., Ley, O., and Mazet, L · 2010
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Approximation accuracy, gradient methods, and error bound for structured convex optimization
Tseng, P · 2010
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Separation of real algebraic sets and the Łojasiewicz exponent
Kurdyka, K. and Spodzieja, S · 2011
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Convergence rates of inexact proximal-gradient methods for convex optimization
Schmidt, M., Roux, N.L., and Bach, F.R · 2011
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Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward-backward splitting, and regularized Gauss-Seidel methods
Attouch, H., Bolte, J., and Svaiter, B · 2013
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Accelerating stochastic gradient descent using predictive variance reduction
Johnson, R. and Zhang, T · 2013
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Proximal alternating linearized minimization for nonconvex and nonsmooth problems
Accelerated proximal gradient methods for nonconvex programming
Li, H. and Lin, Z · 2015
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Identity matters in deep learning
Hardt, M. and Ma, T · 2016
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Linear convergence of gradient and proximal-gradient methods under the Polyak-Łojasiewicz condition
Karimi, H., Nutini, J., and Schmidt, M · 2016
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Li, G. and Kei, T · 2016
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More efficient accelerated proximal algorithm for nonconvex problems
Yao, Q. and Kwok, J.T · 2016
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Bolte, J., Sabach, S., and Teboulle, M · 2014
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Splitting methods with variable metric for kurdyka–łojasiewicz functions and general convergence rates
Frankel, P., Garrigos, G., and Peypouquet, J · 2015
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Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems
Beck, A. and Teboulle, M
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A fast iterative shrinkage-thresholding algorithm for linear inverse problems
Beck, A. and Teboulle, M
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Stochastic variance reduction for nonconvex optimization
Reddi, S., Hefny, A., Sra, S., Poczos, B., and Smola, A
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Proximal stochastic methods for nonsmooth nonconvex finite-sum optimization
Reddi, S., Sra, S., Poczos, B., and Smola, A
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Geometrical properties and accelerated gradient solvers of non-convex phase retrieval
Zhou, Y., Zhang, H., and Liang, Y · 2016
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Improved SVRG for non-strongly-convex or sum-of-non-convex objectives
Zhu, Z. and Yuan, Y · 2016
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