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Nonconvex and nonsmooth optimization problems are frequently encountered in much of statistics, business, science and engineering, but they are not yet widely recognized as a technology in the sense of scalability.
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Proximal alternating minimization and projection methods for nonconvex problems: an approach based on the Kurdyka-Łojasiewicz inequality
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On the complexity of steepest descent, Newton’s and regularized Newton’s methods for nonconvex unconstrained optimization
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Analysis of multi-stage convex relaxation for sparse regularization
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Distributed optimization and statistical learning via the alternating direction method of multipliers
S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein · 2011
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Adaptive cubic overestimation methods for unconstrained optimization. part ii: worst-case function-evaluation complexity
C. Cartis, N. I. M. Gould, and Ph. L. Toint · 2011
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Sparse higher-order principal components analysis
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Solving a low-rank factorization model for matrix completion by a nonlinear successive over-relaxation algorithm
Z. Wen, W. Yin, and Y. Zhang · 2012
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Worst-case complexity of smoothing quadratic regularization methods for non-Lipschitzian optimization
W. Bian and X. Chen · 2013
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An adaptive cubic regularization algorithm for nonconvex optimization with convex constraints and its function-evaluation complexity
C. Cartis, N. I. M. Gould, and Ph. L. Toint · 2013
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Approximate KKT points and a proximity measure for termination
J. Dutta, K. Deb, R. Tulshyan, and R. Arora · 2013
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New analysis and results for the Frank-Wolfe method
R. M. Freund and P. Grigas · 2013
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A general iterative shrinkage and thresholding algorithm for non-convex regularized optimization problems
P. Gong, C. Zhang, Z. Lu, J. Huang, and J. Ye · 2013
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Revisiting Frank-Wolfe: Projection-free sparse convex optimization
Global convergence of splitting methods for nonconvex composite optimization
G. Li and T. K. Pong · 2015
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Convergence of multiblock Bregman ADMM for nonconvex composite problems
F. Wang, W. Cao, and Z. Xu · 2015
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Global convergence of ADMM in nonconvex nonsmooth optimization
Y. Wang, W. Yin, and J. Zeng · 2015
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Alternating proximal gradient method for sparse nonnegative Tucker decomposition
Y. Xu · 2015
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Alternating direction method of multipliers for sparse zero-variance discriminant analysis and principal component analysis
B. Ames and M. Hong · 2016
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M. Jaggi · 2013
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Conditional gradient algorithms for rank one matrix approximations with a sparsity constraint
R. Luss and M. Teboulle · 2013
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Multi-stage convex relaxation for feature selection
T. Zhang · 2013
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Feasible smoothing quadratic regularization method for box constrained non-Lipschitz optimization
W. Bian and X. Chen · 2014
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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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Complexity of unconstrained l 2 l_{2} - l p l_{p} minimization
X. Chen, D. Ge, Z. Wang, and Y. Ye · 2014
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First-order methods of smooth convex optimization with inexact oracle
O. Devolder, G. François, and Yu. Nesterov · 2014
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A trust region algorithm with a worst-case iteration complexity of 𝒪 ( ϵ − 3 / 2 ) \mathcal{O}(\epsilon^{-3/2}) for nonconvex optimization
F. Curtis, D.P. Robinson, and M. Samadi · 2016
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Mini-batch stochastic approximation methods for nonconvex stochastic composite optimization
S. Ghadimi, G. Lan, and H. Zhang · 2016
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M. Hong · 2016
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Iteration complexity analysis of multi-block ADMM for a family of convex minimization without strong convexity
T. Lin, S. Ma, and S. Zhang · 2016
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A smoothing SQP framework for a class of composite ℓ q \ell_{q} minimization over polyhedron
Y. Liu, S. Ma, Y. Dai, and S. Zhang · 2016
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Convergence rate of Frank-Wolfe for non-convex objectives
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Cubic-regularization counterpart of a variable-norm trust-region method for unconstrained minimization
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Scalable robust matrix recovery: Frank-Wolfe meets proximal methods
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Linearly convergent away-step conditional gradient for nonstrongly convex functions
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On the Information-Adaptive Variants of the ADMM: an Iteration Complexity Perspective
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Tensor and its Tucker core: the invariance relationships
B. Jiang, F. Yang, and S. Zhang · 2017
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Global convergence of unmodified 3-block ADMM for a class of convex minimization problems
T. Lin, S. Ma, and S. Zhang · 2017
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Alternating direction method of multipliers for a class of nonconvex and nonsmooth problems with applications to background/foreground extraction
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