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Stochastic Proximal Gradient (SPG) methods have been widely used for solving optimization problems with a simple (possibly non-smooth) regularizer in machine learning and statistics.
Optimization and nonsmooth analysis , volume 5
Frank H Clarke · 1990
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Variational Analysis
R. Tyrrell Rockafellar and Roger J.-B. Wets · 1998
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Local differentiability of distance functions
R.A. Poliquin, Rockafellar R. T., and Thibault L · 2000
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Variable selection via nonconcave penalized likelihood and its oracle properties
Jianqing Fan and Runze Li · 2001
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On fréchet subdifferentials
A Ya Kruger · 2003
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Convex Optimization
Stephen Boyd and Lieven Vandenberghe · 2004
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Enhancing sparsity by reweighted l1 minimization
Emmanuel J. Candès, Michael B. Wakin, and Stephen P. Boyd · 2008
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Nearly unbiased variable selection under minimax concave penalty
Cun-Hui Zhang · 2010
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l 1 / 2 l_{1/2} regularization: A thresholding representation theory and a fast solver
Zongben Xu, Xiangyu Chang, Fengmin Xu, and Hai Zhang · 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
Hedy Attouch, Jérôme Bolte, and Benar Fux Svaiter · 2013
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Fast image deconvolution using closed-form thresholding formulas of l q ( q = 1 / 2 , 2 / 3 ) l_{q}~(q=1/2,2/3) regularization
Wenfei Cao, Jian Sun, and Zongben Xu · 2013
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Gradient methods for minimizing composite functions
Yu. Nesterov · 2013
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Constrained optimization and Lagrange multiplier methods
Dimitri P Bertsekas · 2014
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Proximal alternating linearized minimization for nonconvex and nonsmooth problems
Jérôme Bolte, Shoham Sabach, and Marc Teboulle · 2014
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SAGA: A fast incremental gradient method with support for non-strongly convex composite objectives
Aaron Defazio, Francis R. Bach, and Simon Lacoste-Julien · 2014
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Gradient descent with proximal average for nonconvex and composite regularization
Wenliang Zhong and James T. Kwok · 2014
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Minimization of non-smooth, non-convex functionals by iterative thresholding
Kristian Bredies, Dirk A Lorenz, and Stefan Reiterer · 2015
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Song Han, Huizi Mao, and William J Dally · 2015
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Global convergence of splitting methods for nonconvex composite optimization
Guoyin Li and Ting Kei Pong · 2015
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Accelerated proximal gradient methods for nonconvex programming
Huan Li and Zhouchen Lin · 2015
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Linear and Nonlinear Programming , volume 228
A successive difference-of-convex approximation method for a class of nonconvex nonsmooth optimization problems
Tianxiang Liu, Ting Kei Pong, and Akiko Takeda · 2017
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Stochastic Difference of Convex Algorithm and its Application to Training Deep Boltzmann Machines
Atsushi Nitanda and Taiji Suzuki · 2017
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Stochastic DCA for the large-sum of non-convex functions problem and its application to group variable selection in classification
Hoai An Le Thi, Hoai Minh Le, Duy Nhat Phan, and Bach Tran · 2017
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Zaiyi Chen and Tianbao Yang · 2018
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Stochastic subgradient method converges on tame functions
Damek Davis, Dmitriy Drusvyatskiy, Sham Kakade, and Jason D Lee · 2018
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David G Luenberger and Yinyu Ye · 2015
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Minimizing nonconvex non-separable functions
Yaoliang Yu, Xun Zheng, Micol Marchetti-Bowick, and Eric P. Xing · 2015
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An inertial forward–backward algorithm for the minimization of the sum of two nonconvex functions
Radu Ioan Bot, Ernö Robert Csetnek, and Szilárd Csaba László · 2016
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Mini-batch stochastic approximation methods for nonconvex stochastic composite optimization
Saeed Ghadimi, Guanghui Lan, and Hongchao Zhang · 2016
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Douglas-rachford splitting for nonconvex optimization with application to nonconvex feasibility problems
Guoyin Li and Ting Kei Pong · 2016
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Proximal stochastic methods for nonsmooth nonconvex finite-sum optimization
Sashank J Reddi, Suvrit Sra, Barnabás Póczos, and Alexander J Smola · 2016
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Quantized convolutional neural networks for mobile devices
Jiaxiang Wu, Cong Leng, Yuhang Wang, Qinghao Hu, and Jian Cheng · 2016
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A simple proximal stochastic gradient method for nonsmooth nonconvex optimization
Zhize Li and Jian Li · 2018
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Catalyst for gradient-based nonconvex optimization
Courtney Paquette, Hongzhou Lin, Dmitriy Drusvyatskiy, Julien Mairal, and Zaid Harchaoui · 2018
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Model compression via distillation and quantization
Antonio Polino, Razvan Pascanu, and Dan Alistarh · 2018
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Zhe Wang, Kaiyi Ji, Yi Zhou, Yingbin Liang, and Vahid Tarokh · 2018
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Lei Yang · 2018
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Stochastic nested variance reduced gradient descent for nonconvex optimization
Dongruo Zhou, Pan Xu, and Quanquan Gu · 2018
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Stochastic model-based minimization of weakly convex functions
Damek Davis and Dmitriy Drusvyatskiy · 2019
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Stochastic gradient methods for non-smooth non-convex regularized optimization
Michael R Metel and Akiko Takeda · 2019
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Nhan H Pham, Lam M Nguyen, Dzung T Phan, and Quoc Tran-Dinh · 2019
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Lower bounds for smooth nonconvex finite-sum optimization
Dongruo Zhou and Quanquan Gu · 2019
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