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Journal of the American Statistical Association, ISSN 0162-1459, 09/2011, Volume 106, Issue 495, pp. 1125 - 1138
Journal Article
Digital Signal Processing, ISSN 1051-2004, 12/2018, Volume 83, pp. 165 - 179
This paper proposes vector minimax concave (VMC) penalty for sparse representation using tools of Moreau envelope. The VMC penalty is a weighted MC function;... 
Minimax-concave penalty | CEL0 | Sparse representation | Nonconvex sparsity regularization | APPROXIMATION | RECONSTRUCTION | ALGORITHM | DECOMPOSITION | SIGNALS | L-1/2 REGULARIZATION | VARIABLE SELECTION | ENGINEERING, ELECTRICAL & ELECTRONIC | ALTERNATING DIRECTION METHOD | CONVERGENCE | CELO | FAULTS | Analysis | Algorithms
Journal Article
SIAM Journal on Optimization, ISSN 1052-6234, 2016, Volume 26, Issue 3, pp. 1465 - 1492
We consider a class of constrained optimization problems with a possibly nonconvex non-Lipschitz objective and a convex feasible set being the intersection of... 
Exact penalty | Nonconvex optimization | Sparse solution | Non-Lipschitz optimization | Proximal gradient method | MATHEMATICS, APPLIED | NONCONVEX MINIMIZATION | RECONSTRUCTION | nonconvex optimization | ALGORITHMS | proximal gradient method | VARIABLE SELECTION | sparse solution | exact penalty | MODELS | non-Lipschitz optimization | IMAGES | ESTIMATORS | SYSTEMS | NONSMOOTH
Journal Article
SIAM Journal on Imaging Sciences, 07/2015, Volume 8, Issue 3, pp. 1607 - 1639
Within the framework of the l0 regularized least squares problem, we focus, in this paper, on nonconvex continuous penalties approximating the l0 -norm. Such... 
Underdetermined linear systems | Continuous exact ℓ | Inverse problems | Minimizer equivalence | Sparse modeling | penalty | Nonconvex nonsmooth penalty | regularization | Global minimizers | Local minimizers | Mathematics | Optimization and Control | Engineering Sciences | Image Processing | Computer Science | Signal and Image processing
Journal Article
Journal of Scientific Computing, ISSN 0885-7474, 2/2019, Volume 78, Issue 2, pp. 1063 - 1086
Journal Article
Mechanical Systems and Signal Processing, ISSN 0888-3270, 07/2019, Volume 127, pp. 202 - 233
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 2012, Volume 75, Issue 3, pp. 1158 - 1167
Given an augmented Lagrangian scheme for a general optimization problem, we use an epsilon subgradient step for improving the dual function. This can be seen... 
Kissing number problem | Nonsmooth optimization | Nonconvex optimization | Duality scheme | Penalty method | Augmented Lagrangian | MATHEMATICS | MATHEMATICS, APPLIED | HARD-SPHERES PROBLEMS | MODIFIED SUBGRADIENT ALGORITHM | IMPLEMENTATION | DUALITY | Penalty function | Illustrations | Infinity | Nonlinearity | Kissing | Optimization | Convergence
Journal Article
Numerical Algorithms, ISSN 1017-1398, 05/2017, Volume 75, Issue 1, pp. 305 - 336
We present a competitive algorithm to minimize a locally Lipschitz function constrained with locally Lipschitz constraints. The approach is to use an l(1)... 
Conjugate gradient | Nonsmooth optimization | Goldstein subdifferential | Constrained problem | NONCONVEX OPTIMIZATION | NONLINEAR OPTIMIZATION | MATHEMATICS, APPLIED | CONVEX NONDIFFERENTIABLE MINIMIZATION | BUNDLE METHODS | GRADIENT SAMPLING ALGORITHM | CONVERGENCE | UNCONSTRAINED MINIMIZATION
Journal Article
Neural Networks, ISSN 0893-6080, 01/2016, Volume 73, pp. 10 - 25
Journal Article
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, ISSN 1751-8113, 10/2019, Volume 52, Issue 41, p. 414003
We investigate the signal reconstruction performance of sparse linear regression in the presence of noise when piecewise continuous nonconvex penalties are... 
sparse linear regression | compressed sensing | PHYSICS, MULTIDISCIPLINARY | replica method | nonconvex penalty | cross-validation | ALGORITHMS | PHYSICS, MATHEMATICAL | VARIABLE SELECTION | LIKELIHOOD
Journal Article
IEEE Transactions on Signal Processing, ISSN 1053-587X, 12/2016, Volume 64, Issue 24, pp. 6650 - 6664
Journal Article
Journal of Electronic Imaging, ISSN 1017-9909, 9/2017, Volume 26, Issue 5, pp. 053005 - 053005
Journal Article