A notion of total variation depending on a metric with discontinuous coefficients, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.11, issue.1, pp.91-133, 1994. ,
DOI : 10.1016/S0294-1449(16)30197-4
Mathematical Problems in Image Processing, 2006. ,
A Dykstra-like algorithm for two monotone operators, Pacific J. Optim, vol.4, pp.383-391, 2008. ,
The Baillon-Haddad theorem revisited, J. Convex Anal, vol.17, 2010. ,
Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces, 2011. ,
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems, SIAM Journal on Imaging Sciences, vol.2, issue.1, pp.183-202, 2009. ,
DOI : 10.1137/080716542
A l 1-Unified Variational Framework for Image Restoration, Proc. Eighth Europ. Conf. Comput. Vision, Prague, pp.1-13, 2004. ,
DOI : 10.1007/978-3-540-24673-2_1
URL : https://hal.archives-ouvertes.fr/hal-00217251
A Dual Approach to Multidimensional $L_p$ Spectral Estimation Problems, SIAM Journal on Control and Optimization, vol.26, issue.4, pp.985-996, 1988. ,
DOI : 10.1137/0326053
Probing the Pareto Frontier for Basis Pursuit Solutions, SIAM Journal on Scientific Computing, vol.31, issue.2, pp.890-912, 2008. ,
DOI : 10.1137/080714488
Linear inverse problems with discrete data. I. General formulation and singular system analysis, Inverse Problems, vol.1, issue.4, pp.301-330, 1985. ,
DOI : 10.1088/0266-5611/1/4/004
A New TwIST: Two-Step Iterative Shrinkage/Thresholding Algorithms for Image Restoration, IEEE Transactions on Image Processing, vol.16, issue.12, pp.2992-3004, 2007. ,
DOI : 10.1109/TIP.2007.909319
Maximum Entropy Reconstruction Using Derivative Information, Part 1: Fisher Information and Convex Duality, Mathematics of Operations Research, vol.21, issue.2, pp.442-468, 1996. ,
DOI : 10.1287/moor.21.2.442
Duality and convex programming, in : Handbook of Imaging, O. Scherzer Ed, pp.229-270, 2011. ,
Linear Convergence of Iterative Soft-Thresholding, Journal of Fourier Analysis and Applications, vol.157, issue.1, pp.813-837, 2008. ,
DOI : 10.1007/s00041-008-9041-1
Convex variational formulation with smooth coupling for multicomponent signal decomposition and recovery, Numer. Math. Theory Methods Appl, vol.2, pp.485-508, 2009. ,
Convergence analysis of tight framelet approach for missing data recovery, Advances in Computational Mathematics, vol.41, issue.3, pp.87-113, 2009. ,
DOI : 10.1007/s10444-008-9084-5
A framelet-based image inpainting algorithm, Applied and Computational Harmonic Analysis, vol.24, issue.2, pp.131-149, 2008. ,
DOI : 10.1016/j.acha.2007.10.002
A multiprojection algorithm using Bregman projections in a product space, Numerical Algorithms, vol.17, issue.2, pp.221-239, 1994. ,
DOI : 10.1007/BF02142692
Parallel Optimization : Theory, Algorithms and Applications, 1997. ,
An algorithm for total variation minimization and applications, J. Math. Imaging Vision, vol.20, pp.89-97, 2004. ,
Total Variation Minimization and a Class of Binary MRF Models, Lecture Notes in Comput. Sci, vol.3757, pp.136-152, 2005. ,
DOI : 10.1007/11585978_10
A First-Order Primal-Dual Algorithm for Convex Problems with??Applications to Imaging, Journal of Mathematical Imaging and Vision, vol.60, issue.5, pp.120-145, 2011. ,
DOI : 10.1007/s10851-010-0251-1
URL : https://hal.archives-ouvertes.fr/hal-00490826
A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration, SIAM Journal on Scientific Computing, vol.20, issue.6, pp.1964-1977, 1999. ,
DOI : 10.1137/S1064827596299767
A variational formulation for frame-based inverse problems, Inverse Problems, vol.23, issue.4, pp.1495-1518, 2007. ,
DOI : 10.1088/0266-5611/23/4/008
URL : https://hal.archives-ouvertes.fr/hal-00621883
Nested Iterative Algorithms for Convex Constrained Image Recovery Problems, SIAM Journal on Imaging Sciences, vol.2, issue.2, pp.730-762, 2009. ,
DOI : 10.1137/080727749
URL : https://hal.archives-ouvertes.fr/hal-00621932
A proximal-based decomposition method for convex minimization problems, Mathematical programming, pp.81-101, 1994. ,
DOI : 10.1007/BF01582566
Signal recovery by best feasible approximation, IEEE Transactions on Image Processing, vol.2, issue.2, pp.269-271, 1993. ,
DOI : 10.1109/83.217232
Inconsistent signal feasibility problems: least-squares solutions in a product space, IEEE Transactions on Signal Processing, vol.42, issue.11, pp.2955-2966, 1994. ,
DOI : 10.1109/78.330356
The convex feasibility problem in image recovery, in Advances in Imaging and Electron Physics, pp.155-270, 1996. ,
Dualization of signal recovery problems, preprint Dualization of signal recovery problems, Set- Valued Var, ØØÔÔ»»»ÖÜÜÚºÓÖÖ»»»×»¼¼¼¼º¼¼¿¿ [34] P. L. Combettes, D -inh D?ungD?ung, and B. C. V?uV?u, pp.373-404, 2009. ,
Proximal Thresholding Algorithm for Minimization over Orthonormal Bases, SIAM Journal on Optimization, vol.18, issue.4, pp.1351-1376, 2007. ,
DOI : 10.1137/060669498
URL : https://hal.archives-ouvertes.fr/hal-00621819
A Douglas???Rachford Splitting Approach to Nonsmooth Convex Variational Signal Recovery, IEEE Journal of Selected Topics in Signal Processing, vol.1, issue.4, pp.564-574, 2007. ,
DOI : 10.1109/JSTSP.2007.910264
URL : https://hal.archives-ouvertes.fr/hal-00621820
A proximal decomposition method for solving convex variational inverse problems, Inverse Problems, vol.24, issue.6, 2008. ,
DOI : 10.1088/0266-5611/24/6/065014
URL : https://hal.archives-ouvertes.fr/hal-00692901
The use of noise properties in set theoretic estimation, IEEE Transactions on Signal Processing, vol.39, issue.7, pp.1630-1641, 1991. ,
DOI : 10.1109/78.134400
Signal Recovery by Proximal Forward-Backward Splitting, Multiscale Modeling & Simulation, vol.4, issue.4, pp.1168-1200, 2005. ,
DOI : 10.1137/050626090
URL : https://hal.archives-ouvertes.fr/hal-00017649
An iterative thresholding algorithm for linear inverse problems with a sparsity constraint, Communications on Pure and Applied Mathematics, vol.58, issue.11, pp.1413-1457, 2004. ,
DOI : 10.1002/cpa.20042
Iteratively solving linear inverse problems under general convex constraints, Inverse Problems and Imaging, vol.1, issue.1, pp.29-46, 2007. ,
DOI : 10.3934/ipi.2007.1.29
A dual algorithm for denoising and preserving edges in image processing, Journal of Inverse and Ill-posed Problems, vol.15, issue.2, pp.149-165, 2007. ,
DOI : 10.1515/JIIP.2007.008
Ideal spatial adaptation by wavelet shrinkage, Biometrika, vol.81, issue.3, pp.425-455, 1994. ,
DOI : 10.1093/biomet/81.3.425
Denoising of Frame Coefficients Using $\ell^1$ Data-Fidelity Term and Edge-Preserving Regularization, Multiscale Modeling & Simulation, vol.6, issue.2, pp.547-576, 2007. ,
DOI : 10.1137/06065828X
Total Variation Projection With First Order Schemes, IEEE Transactions on Image Processing, vol.20, issue.3, pp.657-669, 2011. ,
DOI : 10.1109/TIP.2010.2072512
URL : https://hal.archives-ouvertes.fr/hal-00401251
Domain decomposition methods for linear inverse problems with sparsity constraints, Inverse Problems, vol.23, issue.6, pp.2505-2526, 2007. ,
DOI : 10.1088/0266-5611/23/6/014
Super-resolution through Error Energy Reduction, Optica Acta: International Journal of Optics, vol.19, issue.9, pp.709-720, 1974. ,
DOI : 10.1080/713818946
An Infeasible Primal-Dual Algorithm for Total Bounded Variation--Based Inf-Convolution-Type Image Restoration, SIAM Journal on Scientific Computing, vol.28, issue.1, pp.1-23, 2006. ,
DOI : 10.1137/040613263
A Fast Total Variation Minimization Method for Image Restoration, Multiscale Modeling & Simulation, vol.7, issue.2, pp.774-795, 2008. ,
DOI : 10.1137/070703533
A regularized dual-based iterative method for a class of image reconstruction problems, Inverse Problems, vol.9, issue.6, pp.679-696, 1993. ,
DOI : 10.1088/0266-5611/9/6/006
Comparison of formulations and solution methods for image restoration problems, Inverse Problems, vol.17, issue.6, pp.1977-1995, 2001. ,
DOI : 10.1088/0266-5611/17/6/326
An optimal technique for constraint-based image restoration and reconstruction, IEEE Transactions on Acoustics, Speech, and Signal Processing, vol.34, issue.6, pp.1629-1642, 1986. ,
DOI : 10.1109/TASSP.1986.1165001
Fitting a bandlimited signal to given points, IEEE Transactions on Information Theory, vol.11, issue.3, pp.372-376, 1965. ,
DOI : 10.1109/TIT.1965.1053777
A Wavelet Tour of Signal Processing, 1999. ,
Image reconstruction from limited data : Theory and applications in computerized tomography, Image Recovery : Theory and Application, pp.321-368, 1987. ,
Inéquations Variationnelles de la Mécanique (Publications Mathématiques d'Orsay , no. 80.01), 1980. ,
Fonctions convexes duales et points proximaux dans un espace hilbertien, C. R. Acad. Sci. Paris Sér. A Math, vol.255, pp.2897-2899, 1962. ,
Séminaire sur les Équations aux Dérivées Partielles II, pp.1966-1967 ,
Problem Complexity and Method Efficiency in Optimization, 1983. ,
Smooth minimization of non-smooth functions, Math. Program, vol.103, pp.127-152, 2005. ,
Reconstruction with Noisy Data: An Approach via Eigenvalue Optimization, SIAM Journal on Optimization, vol.8, issue.1, pp.82-104, 1998. ,
DOI : 10.1137/S105262349629856X
A new algorithm in spectral analysis and band-limited extrapolation, IEEE Transactions on Circuits and Systems, vol.22, issue.9, pp.735-742, 1975. ,
DOI : 10.1109/TCS.1975.1084118
Computational Methods in Optimization : A Unified Approach, 1971. ,
A Dual Approach to Linear Inverse Problems with Convex Constraints, SIAM Journal on Control and Optimization, vol.31, issue.4, pp.1080-1092, 1993. ,
DOI : 10.1137/0331049
Duality and stability in extremum problems involving convex functions, Pacific Journal of Mathematics, vol.21, issue.1, pp.167-187, 1967. ,
DOI : 10.2140/pjm.1967.21.167
Convex Analysis, 1970. ,
DOI : 10.1515/9781400873173
Nonlinear total variation based noise removal algorithms, Physica D: Nonlinear Phenomena, vol.60, issue.1-4, pp.259-268, 1992. ,
DOI : 10.1016/0167-2789(92)90242-F
Image Recovery : Theory and Application, 1987. ,
Spectral estimation via minimum energy correlation extension, IEEE Transactions on Acoustics, Speech, and Signal Processing, vol.33, issue.6, pp.1509-1515, 1985. ,
DOI : 10.1109/TASSP.1985.1164735
Just relax: convex programming methods for identifying sparse signals in noise, IEEE Transactions on Information Theory, vol.52, issue.3, pp.1030-1051, 2006. ,
DOI : 10.1109/TIT.2005.864420
The feasible solution in signal restoration, IEEE Transactions on Acoustics, Speech, and Signal Processing, vol.32, issue.2, pp.201-212, 1984. ,
DOI : 10.1109/TASSP.1984.1164297
The application of numerical filtering to the solution of integral equations encountered in indirect sensing measurements, Journal of the Franklin Institute, vol.279, issue.2, pp.95-109, 1965. ,
DOI : 10.1016/0016-0032(65)90209-7
Filtering noise from images with wavelet transforms, Magnetic Resonance in Medicine, vol.110, issue.2, pp.288-295, 1991. ,
DOI : 10.1002/mrm.1910210213
Efficient Schemes for Total Variation Minimization Under Constraints in Image Processing, SIAM Journal on Scientific Computing, vol.31, issue.3, pp.2047-2080, 2009. ,
DOI : 10.1137/070696143
URL : https://hal.archives-ouvertes.fr/inria-00166096
Generalized Image Restoration by the Method of Alternating Orthogonal Projections, IEEE Transactions on Circuits and Systems, vol.25, issue.9, pp.694-702, 1978. ,
DOI : 10.1109/TCS.1978.1084541
Extensions of a result on the synthesis of signals in the presence of inconsistent constraints, IEEE Transactions on Circuits and Systems, vol.33, issue.4, pp.465-468, 1986. ,
DOI : 10.1109/TCS.1986.1085927
Image Restoration by the Method of Convex Projections: Part 1ߞTheory, IEEE Transactions on Medical Imaging, vol.1, issue.2, pp.81-94, 1982. ,
DOI : 10.1109/TMI.1982.4307555
Dykstra???s Alternating Projection Algorithm for Two Sets, Journal of Approximation Theory, vol.79, issue.3, pp.418-443, 1994. ,
DOI : 10.1006/jath.1994.1136
Total Variation Minimization and a Class of Binary MRF Models, Lecture Notes in Comput. Sci, vol.3757, pp.136-152, 2005. ,
DOI : 10.1007/11585978_10
Iterative construction of the resolvent of a sum of maximal monotone operators, J. Convex Anal, vol.16, pp.727-748, 2009. ,
Dualization of signal recovery problems, Set-Valued Var, Anal, vol.18, pp.373-404, 2010. ,
Proximal Thresholding Algorithm for Minimization over Orthonormal Bases, SIAM Journal on Optimization, vol.18, issue.4, pp.1351-1376, 2007. ,
DOI : 10.1137/060669498
URL : https://hal.archives-ouvertes.fr/hal-00621819
Proximal splitting methods in signal processing, in Fixed-Point Algorithms for, Inverse Problems in Science and Engineering ,
Signal Recovery by Proximal Forward-Backward Splitting, Multiscale Modeling & Simulation, vol.4, issue.4, pp.1168-1200, 2005. ,
DOI : 10.1137/050626090
URL : https://hal.archives-ouvertes.fr/hal-00017649
Elastic-net regularization in learning theory, Journal of Complexity, vol.25, issue.2, pp.201-230, 2009. ,
DOI : 10.1016/j.jco.2009.01.002
Best Approximation in Inner Product Spaces, 2001. ,
DOI : 10.1007/978-1-4684-9298-9
A cyclic projection algorithm via duality, Metrika, vol.68, issue.1, pp.29-54, 1989. ,
DOI : 10.1007/BF02614077
Inéquations Variationnelles de la Mécanique (Publications Mathématiques d'Orsay, no. 80.01), 1980. ,
Fonctions convexes duales et points proximaux dans un espace hilbertien, C. R. Acad. Sci. Paris Sér. A Math, vol.255, pp.2897-2899, 1962. ,
A Dual Approach to Linear Inverse Problems with Convex Constraints, SIAM Journal on Control and Optimization, vol.31, issue.4, pp.1080-1092, 1993. ,
DOI : 10.1137/0331049
Variational Analysis, 3rd printing, 2009. ,
Nonlinear total variation based noise removal algorithms, Physica D: Nonlinear Phenomena, vol.60, issue.1-4, pp.259-268, 1992. ,
DOI : 10.1016/0167-2789(92)90242-F
Applications of a Splitting Algorithm to Decomposition in Convex Programming and Variational Inequalities, SIAM Journal on Control and Optimization, vol.29, issue.1, pp.119-138, 1991. ,
DOI : 10.1137/0329006
Regularization and variable selection via the elastic net, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.5, issue.2, pp.301-320, 2005. ,
DOI : 10.1073/pnas.201162998
Alternating proximal algorithms for weakly coupled convex minimization problems ? Applications to dynamical games and PDE's, J. Convex Anal, vol.15, pp.485-506, 2008. ,
A Parallel Splitting Method for Coupled Monotone Inclusions, SIAM Journal on Control and Optimization, vol.48, issue.5, pp.3246-3270, 2010. ,
DOI : 10.1137/090754297
A general duality principle for the sum of two operators, J. Convex Anal, vol.3, pp.1-24, 1996. ,
Quelques propri??t??s des op??rateurs angle-born??s etn-cycliquement monotones, Israel Journal of Mathematics, vol.17, issue.2, pp.137-150, 1977. ,
DOI : 10.1007/BF03007664
The Baillon-Haddad theorem revisited, J. Convex Anal, vol.17, pp.781-787, 2010. ,
Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces, 2011. ,
A Monotone+Skew Splitting Model for Composite Monotone Inclusions in Duality, SIAM Journal on Optimization, vol.21, issue.4, pp.1230-1250, 2011. ,
DOI : 10.1137/10081602X
Monotone Operator Methods for Nash Equilibria in Non-potential Games, Computational and Analytical Mathematics, 2013. ,
DOI : 10.1007/978-1-4614-7621-4_9
Simultaneous cartoon and texture inpainting, Inverse Problems and Imaging, vol.4, issue.3, pp.379-395, 2010. ,
DOI : 10.3934/ipi.2010.4.379
A First-Order Primal-Dual Algorithm for Convex Problems with??Applications to Imaging, Journal of Mathematical Imaging and Vision, vol.60, issue.5, pp.120-145, 2011. ,
DOI : 10.1007/s10851-010-0251-1
URL : https://hal.archives-ouvertes.fr/hal-00490826
Convergence Rates in Forward--Backward Splitting, SIAM Journal on Optimization, vol.7, issue.2, pp.421-444, 1997. ,
DOI : 10.1137/S1052623495290179
A proximal-based decomposition method for convex minimization problems, Mathematical Programming, vol.29, issue.1-3, pp.81-101, 1994. ,
DOI : 10.1007/BF01582566
Solving monotone inclusions via compositions of nonexpansive averaged operators, Optimization, pp.475-504, 2004. ,
Proximity for sums of composite functions, Journal of Mathematical Analysis and Applications, vol.380, issue.2, pp.680-688, 2011. ,
DOI : 10.1016/j.jmaa.2011.02.079
URL : https://hal.archives-ouvertes.fr/hal-00643804
Proximal Splitting Methods in Signal Processing ,
DOI : 10.1007/978-1-4419-9569-8_10
URL : https://hal.archives-ouvertes.fr/hal-00643807
Primal-dual splitting algorithm for solving inclusions with mixtures of composite, Lipschitzian, and parallel-sum type monotone operators, Set-Valued Var, Anal, vol.20, pp.307-330, 2012. ,
Signal Recovery by Proximal Forward-Backward Splitting, Multiscale Modeling & Simulation, vol.4, issue.4, pp.1168-1200, 2005. ,
DOI : 10.1137/050626090
URL : https://hal.archives-ouvertes.fr/hal-00017649
A generic first-order primal-dual method for convex optimization involving Lipschitzian, proximable and linear composite terms, 2011. ,
Finite-Dimensional Variational Inequalities and Complementarity Problems, 2003. ,
Applications of the method of multipliers to variational inequalities Augmented Lagrangian Methods : Applications to the Numerical Solution of Boundary Value Problems, pp.299-331, 1983. ,
Augmented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics, 1989. ,
DOI : 10.1137/1.9781611970838
Convergence Analysis of Primal-Dual Algorithms for a Saddle-Point Problem: From Contraction Perspective, SIAM Journal on Imaging Sciences, vol.5, issue.1, pp.119-149, 2012. ,
DOI : 10.1137/100814494
Topics in Finite Element Solution of Elliptic Problems (Lectures on Mathematics, Tata Institute of Fundamental Research, issue.63, 1979. ,
Dual variational inequalities, Journal of Mathematical Analysis and Applications, vol.40, issue.1, pp.202-206, 1972. ,
DOI : 10.1016/0022-247X(72)90043-1
A parallel inertial proximal optimization method, Pacific Journal of Optimization, vol.8, issue.2, pp.273-305, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00790702
A Generalized Forward-Backward Splitting, SIAM Journal on Imaging Sciences, vol.6, issue.3, 2011. ,
DOI : 10.1137/120872802
URL : https://hal.archives-ouvertes.fr/hal-00613637
Duality and stability in extremum problems involving convex functions, Pacific Journal of Mathematics, vol.21, issue.1, pp.167-187, 1967. ,
DOI : 10.2140/pjm.1967.21.167
Further applications of a splitting algorithm to decomposition in variational inequalities and convex programming, Mathematical Programming, vol.7, issue.1-3, pp.249-263, 1990. ,
DOI : 10.1007/BF01582258
Applications of a Splitting Algorithm to Decomposition in Convex Programming and Variational Inequalities, SIAM Journal on Control and Optimization, vol.29, issue.1, pp.119-138, 1991. ,
DOI : 10.1137/0329006
Co-Coercivity and Its Role in the Convergence of Iterative Schemes for Solving Variational Inequalities, SIAM Journal on Optimization, vol.6, issue.3, pp.714-726, 1996. ,
DOI : 10.1137/S1052623494250415
On the projected subgradient method for nonsmooth convex optimization in a Hilbert space, Mathematical Programming, vol.19, issue.1, pp.23-35, 1998. ,
DOI : 10.1007/BF01584842
On Projection Algorithms for Solving Convex Feasibility Problems, SIAM Review, vol.38, issue.3, pp.367-426, 1996. ,
DOI : 10.1137/S0036144593251710
Bregman Monotone Optimization Algorithms, SIAM Journal on Control and Optimization, vol.42, issue.2, pp.596-636, 2003. ,
DOI : 10.1137/S0363012902407120
A Weak-to-Strong Convergence Principle for Fej??r-Monotone Methods in Hilbert Spaces, Mathematics of Operations Research, vol.26, issue.2, pp.248-264, 2001. ,
DOI : 10.1287/moor.26.2.248.10558
Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces, 2011. ,
Extrapolation algorithm for affine-convex feasibility problems, Numerical Algorithms, vol.25, issue.3, pp.239-274, 2006. ,
DOI : 10.1007/s11075-005-9010-6
URL : https://hal.archives-ouvertes.fr/hal-00017644
A family of variable metric proximal methods, Mathematical Programming, vol.14, issue.1-3, pp.15-47, 1995. ,
DOI : 10.1007/BF01585756
URL : https://hal.archives-ouvertes.fr/inria-00074821
The method of successive projection for finding a common point of convex sets, Soviet Math. Dokl, vol.6, pp.688-692, 1965. ,
Convergence theorems for sequences of nonlinear operators in Banach spaces, Mathematische Zeitschrift, vol.86, issue.83, pp.201-225, 1967. ,
DOI : 10.1007/BF01109805
A Variable Metric Proximal Point Algorithm for Monotone Operators, SIAM Journal on Control and Optimization, vol.37, issue.2, pp.353-375, 1999. ,
DOI : 10.1137/S0363012992235547
Convergence Rates in Forward--Backward Splitting, SIAM Journal on Optimization, vol.7, issue.2, pp.421-444, 1997. ,
DOI : 10.1137/S1052623495290179
Quasi-Fej??rian Analysis of Some Optimization Algorithms, pp.115-152, 2001. ,
DOI : 10.1016/S1570-579X(01)80010-0
Solving monotone inclusions via compositions of nonexpansive averaged operators, Optimization, pp.475-504, 2004. ,
Fej??r Monotonicity in Convex Optimization, pp.1016-1024, 2009. ,
DOI : 10.1007/978-0-387-74759-0_179
Proximal Thresholding Algorithm for Minimization over Orthonormal Bases, SIAM Journal on Optimization, vol.18, issue.4, pp.1351-1376, 2007. ,
DOI : 10.1137/060669498
URL : https://hal.archives-ouvertes.fr/hal-00621819
Variable metric forward-backward splitting with applications to monotone inclusions in duality, Optimization, to appear, 2013. ,
Signal Recovery by Proximal Forward-Backward Splitting, Multiscale Modeling & Simulation, vol.4, issue.4, pp.1168-1200, 2005. ,
DOI : 10.1137/050626090
URL : https://hal.archives-ouvertes.fr/hal-00017649
Fejér mappings and convex programming, Siberian Math, J, vol.10, pp.762-772, 1969. ,
Fej??r processes in theory and practice: Recent results, Russian Mathematics, vol.53, issue.1, pp.36-55, 2009. ,
DOI : 10.3103/S1066369X09010022
Random Fejér and quasi-Fejér sequences, Theory of Optimal Solutions? Akademiya Nauk Ukrainsko? ? SSR Kiev, Selected Translations in Mathematical Statistics and Probability, pp.76-83, 1968. ,
???ber die Lage der Nullstellen von Polynomen, die aus Minimumforderungen gewisser Art entspringen, Mathematische Annalen, vol.85, issue.1, pp.41-48, 1922. ,
DOI : 10.1007/BF01449600
The method of projections for finding the common point of convex sets, USSR Computational Mathematics and Mathematical Physics, vol.7, issue.6, pp.1-24, 1967. ,
DOI : 10.1016/0041-5553(67)90113-9
An alternating projection that does not converge in norm, Nonlinear Analysis: Theory, Methods & Applications, vol.57, issue.1, pp.35-61, 2004. ,
DOI : 10.1016/j.na.2003.11.004
Perturbation Theory for Linear Operators, 1980. ,
Infinite Sequences and Series, 1956. ,
A class of variable metric decomposition methods for monotone variational inclusions, J. Convex Anal, vol.16, pp.857-880, 2009. ,
The relaxation method for linear inequalities, Journal canadien de math??matiques, vol.6, issue.0, pp.393-404, 1954. ,
DOI : 10.4153/CJM-1954-038-x
Strong convergence of contraction semigroups and of iterative methods for accretive operators in Banach spaces, Israel Journal of Mathematics, vol.14, issue.1, pp.44-58, 1979. ,
DOI : 10.1007/BF02761184
A Class of Inexact Variable Metric Proximal Point Algorithms, SIAM Journal on Optimization, vol.19, issue.1, pp.240-260, 2008. ,
DOI : 10.1137/070688146
Introduction to Optimization. Optimization Software Inc, 1987. ,
A class of iterative methods with Fejér-monotone sequences, Eesti NSV Tead. Akad. Toimetised Füüs.-Mat, vol.18, pp.22-26, 1969. ,
Weak convergence theorems for nonexpansive mappings in Banach spaces, Journal of Mathematical Analysis and Applications, vol.67, issue.2, pp.274-276, 1979. ,
DOI : 10.1016/0022-247X(79)90024-6
Monotone Operators and the Proximal Point Algorithm, SIAM Journal on Control and Optimization, vol.14, issue.5, pp.877-898, 1976. ,
DOI : 10.1137/0314056
A general iterative scheme with applications to convex optimization and related fields, Optimization, pp.885-902, 1991. ,
A Parallel Splitting Method for Coupled Monotone Inclusions, SIAM Journal on Control and Optimization, vol.48, issue.5, pp.3246-3270, 2010. ,
DOI : 10.1137/090754297
A general duality principle for the sum of two operators, J. Convex Anal, vol.3, pp.1-24, 1996. ,
Bregman Monotone Optimization Algorithms, SIAM Journal on Control and Optimization, vol.42, issue.2, pp.596-636, 2003. ,
DOI : 10.1137/S0363012902407120
Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces, 2011. ,
A family of variable metric proximal methods, Mathematical Programming, vol.14, issue.1-3, pp.15-47, 1995. ,
DOI : 10.1007/BF01585756
URL : https://hal.archives-ouvertes.fr/inria-00074821
Conjugate Duality in Convex Optimization, Lecture Notes in Economics and Mathematical Systems, vol.637, 2010. ,
Monotone Operator Methods for Nash Equilibria in Non-potential Games, Computational and Analytical Mathematics ,
DOI : 10.1007/978-1-4614-7621-4_9
A Variable Metric Proximal Point Algorithm for Monotone Operators, SIAM Journal on Control and Optimization, vol.37, issue.2, pp.353-375, 1999. ,
DOI : 10.1137/S0363012992235547
On the superlinear convergence of the variable metric proximal point algorithm using Broyden and BFGS matrix secant updating, Mathematical Programming, vol.88, issue.1, pp.157-181, 2000. ,
DOI : 10.1007/PL00011373
Convergence Rates in Forward--Backward Splitting, SIAM Journal on Optimization, vol.7, issue.2, pp.421-444, 1997. ,
DOI : 10.1137/S1052623495290179
Proximal quasi-Newton methods for nondifferentiable convex optimization, Mathematical Programming, vol.85, issue.2, pp.313-334, 1999. ,
DOI : 10.1007/s101070050059
Solving monotone inclusions via compositions of nonexpansive averaged operators, Optimization, pp.475-504, 2004. ,
Dualization of signal recovery problems, Set- Valued Var, 14] P. L. Combettes, D -inh D?ungD?ung, and B. C. V?uV?u, Proximity for sums of composite functions, pp.373-404, 2010. ,
Proximal splitting methods in signal processing, in Fixed- Point Algorithms for, Inverse Problems in Science and Engineering, pp.185-212, 2011. ,
Primal-dual splitting algorithm for solving inclusions with mixtures of composite, Lipschitzian, and parallel-sum type monotone operators, Set- Valued Var, Anal, vol.20, pp.307-330, 2012. ,
Variable metric quasi-Fej??r monotonicity, Nonlinear Analysis: Theory, Methods & Applications, vol.78, pp.17-31, 2013. ,
DOI : 10.1016/j.na.2012.09.008
Signal Recovery by Proximal Forward-Backward Splitting, Multiscale Modeling & Simulation, vol.4, issue.4, pp.1168-1200, 2005. ,
DOI : 10.1137/050626090
URL : https://hal.archives-ouvertes.fr/hal-00017649
Variable Metric Method for Minimization, SIAM Journal on Optimization, vol.1, issue.1, pp.1-17, 1959. ,
DOI : 10.1137/0801001
A consistent algorithm to solve Lasso, elastic-net and Tikhonov regularization, Journal of Complexity, vol.27, issue.2, pp.188-200, 2011. ,
DOI : 10.1016/j.jco.2011.01.003
Efficient online and batch learning using forward backward splitting, J. Mach. Learn. Res, vol.10, pp.2899-2934, 2009. ,
Smooth methods of multipliers for complementarity problems, Mathematical Programming, vol.86, issue.1, pp.65-90, 1999. ,
DOI : 10.1007/s101079900076
Finite-Dimensional Variational Inequalities and Complementarity Problems, 2003. ,
Augmented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics, SIAM, 1989. ,
DOI : 10.1137/1.9781611970838
Perturbation Theory for Linear Operators, 1980. ,
Variable metric bundle methods: From conceptual to implementable forms, Mathematical Programming, vol.2, issue.3, pp.393-410, 1997. ,
DOI : 10.1007/BF02614390
A class of variable metric decomposition methods for monotone variational inclusions, J. Convex Anal, vol.16, pp.857-880, 2009. ,
Topics in Finite Element Solution of Elliptic Problems (Lectures on Mathematics, Tata Institute of Fundamental Research, issue.63, 1979. ,
Inéquations Variationnelles de la Mécanique (Publications Mathématiques d'Orsay , no. 80.01), 1980. ,
Dual variational inequalities, Journal of Mathematical Analysis and Applications, vol.40, issue.1, pp.202-206, 1972. ,
DOI : 10.1016/0022-247X(72)90043-1
A Class of Inexact Variable Metric Proximal Point Algorithms, SIAM Journal on Optimization, vol.19, issue.1, pp.240-260, 2008. ,
DOI : 10.1137/070688146
Variable metric methods of minimisation, The Computer Journal, vol.12, issue.2, pp.171-178, 1969. ,
DOI : 10.1093/comjnl/12.2.171
Dualization of Generalized Equations of Maximal Monotone Type, SIAM Journal on Optimization, vol.10, issue.3, pp.809-835, 2000. ,
DOI : 10.1137/S1052623498340448
A preconditioning proximal newton method for nondifferentiable convex optimization, Mathematical Programming, vol.2, issue.3, pp.411-429, 1997. ,
DOI : 10.1007/BF02614391
The Variable Metric Proximal Point Algorithm : Theory and Application, 1992. ,
Composition duality and maximal monotonicity, Mathematical Programming, vol.85, issue.1, pp.1-13, 1999. ,
DOI : 10.1007/s101070050043
Duality and stability in extremum problems involving convex functions, Pacific Journal of Mathematics, vol.21, issue.1, pp.167-187, 1967. ,
DOI : 10.2140/pjm.1967.21.167
Further applications of a splitting algorithm to decomposition in variational inequalities and convex programming, Mathematical Programming, vol.7, issue.1-3, pp.249-263, 1990. ,
DOI : 10.1007/BF01582258
Applications of a Splitting Algorithm to Decomposition in Convex Programming and Variational Inequalities, SIAM Journal on Control and Optimization, vol.29, issue.1, pp.119-138, 1991. ,
DOI : 10.1137/0329006
A splitting algorithm for dual monotone inclusions involving cocoercive operators, Adv. Comput. Math, vol.38, pp.667-681, 2013. ,
Co-Coercivity and Its Role in the Convergence of Iterative Schemes for Solving Variational Inequalities, SIAM Journal on Optimization, vol.6, issue.3, pp.714-726, 1996. ,
DOI : 10.1137/S1052623494250415
,n ) n?N , et (c 1,n ) n?N des suites absolument sommables dans H, et pour Combettes, A parallel splitting method for coupled monotone inclusions, SIAM J. Control Optim, vol.48, issue.1, pp.3246-3270, 2010. ,
Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces, 2011. ,
A family of variable metric proximal methods, Mathematical Programming, vol.14, issue.1-3, pp.15-47, 1995. ,
DOI : 10.1007/BF01585756
URL : https://hal.archives-ouvertes.fr/inria-00074821
A Monotone+Skew Splitting Model for Composite Monotone Inclusions in Duality, SIAM Journal on Optimization, vol.21, issue.4, pp.1230-1250, 2011. ,
DOI : 10.1137/10081602X
A Variable Metric Proximal Point Algorithm for Monotone Operators, SIAM Journal on Control and Optimization, vol.37, issue.2, pp.353-375, 1999. ,
DOI : 10.1137/S0363012992235547
On the superlinear convergence of the variable metric proximal point algorithm using Broyden and BFGS matrix secant updating, Mathematical Programming, vol.88, issue.1, pp.157-181, 2000. ,
DOI : 10.1007/PL00011373
Quasi-Fejérian analysis of some optimization algorithms, in Inherently Parallel Algorithms in Feasibility and Optimization and Their Applications, pp.115-152, 2001. ,
Solving monotone inclusions via compositions of nonexpansive averaged operators, Optimization, pp.475-504, 2004. ,
Primal-dual splitting algorithm for solving inclusions with mixtures of composite, Lipschitzian, and parallel-sum type monotone operators, Set-Valued Var, Anal, vol.20, pp.307-330, 2012. ,
Variable metric quasi-Fej??r monotonicity, Nonlinear Analysis: Theory, Methods & Applications, vol.78, pp.17-31, 2013. ,
DOI : 10.1016/j.na.2012.09.008
Variable metric forward-backward splitting with applications to monotone inclusions in duality, Optimization ,
Topics in Finite Element Solution of Elliptic Problems (Lectures on Mathematics, Tata Institute of Fundamental Research, issue.63, 1979. ,
Variable metric bundle methods: From conceptual to implementable forms, Mathematical Programming, vol.2, issue.3, pp.393-410, 1997. ,
DOI : 10.1007/BF02614390
A class of variable metric decomposition methods for monotone variational inclusions, J. Convex Anal, vol.16, pp.857-880, 2009. ,
A Class of Inexact Variable Metric Proximal Point Algorithms, SIAM Journal on Optimization, vol.19, issue.1, pp.240-260, 2008. ,
DOI : 10.1137/070688146
A preconditioning proximal Newton's method for nondifferentiable convex optimization, Math. Program, vol.76, pp.411-430, 1995. ,
Monotone Operators and the Proximal Point Algorithm, SIAM Journal on Control and Optimization, vol.14, issue.5, pp.877-898, 1976. ,
DOI : 10.1137/0314056
Applications of a Splitting Algorithm to Decomposition in Convex Programming and Variational Inequalities, SIAM Journal on Control and Optimization, vol.29, issue.1, pp.119-138, 1991. ,
DOI : 10.1137/0329006
A Modified Forward-Backward Splitting Method for Maximal Monotone Mappings, SIAM Journal on Control and Optimization, vol.38, issue.2, pp.431-446, 2000. ,
DOI : 10.1137/S0363012998338806
C : H ? H un opérateur µ-cocoercif ou µ-lipschitzien monotone, G et Y des espaces hilbertiens réels, r ? G, B : Y ? 2 Y , D : G ? 2 G des opérateurs maximalement monotones tels que D ?1 est ?-cocoercif ou µ-lipschitzien et monotone, ). Le problème est de résoudre l'inclusion primale trouver x ? H tel que z ? Ax + L * (M * BM) ?1 + D ?1 ?1 (Lx ? r) + Cx ,
on peut utiliser la méthode du Chapitre 7 pour résoudre ce problème ,
Combettes, A parallel splitting method for coupled monotone inclusions, SIAM J. Control Optim, vol.48, pp.3246-3270, 2010. ,
Monotone Operator Methods for Nash Equilibria in Non-potential Games, Computational and Analytical Mathematics, 2013. ,
DOI : 10.1007/978-1-4614-7621-4_9
Proximal splitting methods in signal processing, in Fixed-Point Algorithms for, Inverse Problems in Science and Engineering ,
Topics in Finite Element Solution of Elliptic Problems (Lectures on Mathematics, Tata Institute of Fundamental Research, issue.63, 1979. ,