Fetching the paper…
Reading the bibliography…
In this paper, we consider a class of possibly nonconvex, nonsmooth and non-Lipschitz optimization problems arising in many contemporary applications such as machine learning, variable selection and image processing.
Splitting algorithms for the sum of two nonlinear operators
P.L. Lions and B. Mercier · 1979
Earlier work this paper cites.
A generalized proximal point algorithm for certain non-convex minimization problems
M. Fukushima and H. Mine · 1981
Earlier work this paper cites.
A method of solving a convex programming problem with convergence rate O ( 1 / k 2 ) O(1/k^{2})
Y. Nesterov · 1983
Earlier work this paper cites.
A nonmonotone line search technique for Newton’s method
L. Grippo, F. Lampariello, and S. Lucidi · 1986
Earlier work this paper cites.
Regression shrinkage and selection via the Lasso
R. Tibshirani · 1996
Earlier work this paper cites.
Variational Analysis
R.T. Rockafellar and R.J-B. Wets · 1998
Earlier work this paper cites.
Nonmonotone spectral projected gradient methods on convex sets
E.G. Birgin, J.M. Martínez, and M. Raydan · 2000
Earlier work this paper cites.
Asymptotics for lasso-type estimators
K. Knight and W. Fu · 2000
Earlier work this paper cites.
Variable selection via nonconcave penalized likelihood and its oracle properties
J. Fan and R. Li · 2001
Earlier work this paper cites.
On the nonmonotone line search
Y.H. Dai · 2002
Earlier work this paper cites.
Introductory Lectures on Convex Optimization: A Basic Course
Y. Nesterov · 2004
Earlier work this paper cites.
A nonmonotone line search technique and its application to unconstrained optimization
H. Zhang and W.W. Hager · 2004
Earlier work this paper cites.
The Łojasiewicz inequality for nonsmooth subanalytic functions with applications to subgradient dynamical systems
J. Bolte, A. Daniilidis, and A. Lewis · 2007
Earlier work this paper cites.
Asymptotic properties of bridge estimators in sparse high-dimensional regression models
J. Huang, J.L. Horowitz, and S. Ma · 2008
Earlier work this paper cites.
Efficient reconstruction of piecewise constant images using nonsmooth nonconvex minimization
M. Nikolova, M.K. Ng, S. Zhang, and W.-K. Ching · 2008
Earlier work this paper cites.
On accelerated proximal gradient methods for convex-concave optimization
P. Tseng · 2008
Earlier work this paper cites.
On the convergence of the proximal algorithm for nonsmooth functions involving analytic features
H. Attouch and J. Bolte · 2009
Earlier work this paper cites.
Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems
A. Beck and M. Teboulle · 2009
Earlier work this paper cites.
A fast iterative shrinkage-thresholding algorithm for linear inverse problems
A. Beck and M. Teboulle · 2009
Cited alongside, same era.
Sparse reconstruction by separable approximation
S.J. Wright, R. Nowak, and M.A.T. Figueiredo · 2009
Cited alongside, same era.
Proximal alternating minimization and projection methods for nonconvex problems: An approach based on the Kurdyka-Łojasiewicz inequality
H. Attouch, J. Bolte, P. Redont, and A. Soubeyran · 2010
Cited alongside, same era.
Approximation accuracy, gradient methods, and error bound for structured convex optimization
P. Tseng · 2010
Cited alongside, same era.
Nearly unbiased variable selection under minimax concave penalty
C.-H. Zhang · 2010
Cited alongside, same era.
Templates for convex cone problems with applications to sparse signal recovery
Accelerated proximal gradient methods for nonconvex programming
H. Li and Z. Lin · 2015
Later among the works it cites.
Adaptive restart for accelerated gradient schemes
B. O’Donoghue and E.J. Candès · 2015
Later among the works it cites.
Block stochastic gradient iteration for convex and nonconvex optimization
Y. Xu and W. Yin · 2015
Later among the works it cites.
Minimization of ℓ 1 − 2 \ell_{1\mathrm{-}2} for compressed sensing
P. Yin, Y. Lou, Q. He, and J. Xin · 2015
Later among the works it cites.
An introduction to continuous optimization for imaging
A. Chambolle and T. Pock · 2016
Later among the works it cites.
Penalty methods for a class of non-Lipschitz optimization problems
X. Chen, Z. Lu, and T.K. Pong · 2016
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
S. Becker, E.J. Candès, and M.C. Grant · 2011
Cited alongside, same era.
Proximal Splitting Methods in Signal Processing
P.L. Combettes and J.-C. Pesquet · 2011
Cited alongside, same era.
Smoothing methods for nonsmooth, nonconvex minimization
X. Chen · 2012
Cited alongside, same era.
Accelerated multiplicative updates and hierarchical ALS algorithms for nonnegative matrix factorization
N. Gillis and F. Glineur · 2012
Cited alongside, same era.
Optimization for Machine Learning
S. Sra, S. Nowozin, and S.J. Wright · 2012
Cited alongside, same era.
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
Cited alongside, same era.
A general iterative shinkage and thresholding algorithm for non-convex regularized optimization problems
P. Gong, C. Zhang, Z. Lu, J.Z. Huang, and J. Ye · 2013
Cited alongside, same era.
Accelerated gradient methods for nonconvex nonlinear and stochastic programming
S. Ghadimi and G. Lan · 2016
Later among the works it cites.
Difference-of-convex learning: Directional stationarity, optimality, and sparsity
M. Ahn, J.-S. Pang, and J. Xin · 2017
Closest in time.
Optimization methods for supervised machine learning: From linear models to deep learning
F.E. Curtis and K. Scheinberg · 2017
Closest in time.
Further properties of the forward-backward envelope with applications to difference-of-convex programming
Liu. T and T.K. Pong · 2017
Closest in time.
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
Closest in time.
A globally convergent algorithm for nonconvex optimization based on block coordinate update
Y. Xu and W. Yin · 2017
Closest in time.
First-order Splitting Algorithms for Nonconvex Matrix Optimization Problems
L. Yang · 2017
Closest in time.
Calculus of the exponent of Kurdyka–Łojasiewicz inequality and its applications to linear convergence of first–order methods
G. Li and T.K. Pong · 2018
Closest in time.
A proximal difference-of-convex algorithm with extrapolation
B. Wen, X. Chen, and T.K. Pong · 2018
Closest in time.
A non-monotone alternating updating method for a class of matrix factorization problems
L. Yang, T.K. Pong, and X. Chen · 2018
Closest in time.
A successive difference-of-convex approximation method for a class of nonconvex nonsmooth optimization problems
T. Liu, T.K. Pong, and A. Takeda · 2019
Closest in time.