Convergence of the Iterates of Descent Methods for Analytic Cost Functions, SIAM Journal on Optimization, vol.16, issue.2, pp.531-547, 2005. ,
DOI : 10.1137/040605266
Convergence of the Proximal Point Method for Metrically Regular
Mappings, ESAIM: Proceedings, vol.17, pp.1-8, 2007. ,
DOI : 10.1051/proc:071701
URL : https://hal.archives-ouvertes.fr/hal-00507812
On the convergence of the proximal algorithm for nonsmooth functions involving analytic features, Mathematical Programming, vol.4, issue.1-2, pp.5-16, 2009. ,
DOI : 10.1007/s10107-007-0133-5
URL : https://hal.archives-ouvertes.fr/hal-00803898
Alternating Proximal Algorithms for Weakly Coupled Convex Minimization Problems. Applications to Dynamical Games and PDE's, Journal of Convex Analysis, vol.15, pp.485-506, 2008. ,
Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-??ojasiewicz Inequality, Mathematics of Operations Research, vol.35, issue.2, pp.438-457, 2010. ,
DOI : 10.1287/moor.1100.0449
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
Local search proximal algorithms as decision dynamics with costs to move, Set Valued and Variational Analysis, Online First, p.12, 2010. ,
Asymptotic properties of the fenchel dual functional and applications to decomposition problems, Journal of Optimization Theory and Applications, vol.14, issue.3, pp.427-449, 1992. ,
DOI : 10.1007/BF00940050
A Linearly Convergent Algorithm for Solving a Class of Nonconvex/Affine Feasibility Problems to appear in the book Fixed-Point Algorithms for Inverse Problems in Science and Engineering, part of the Springer Verlag series Optimization and Its Applications Available online http, 2010. ,
Real Algebraic and Semialgebraic Sets, des Sciences et des Arts, 1990. ,
Iterative Thresholding for Sparse Approximations, Journal of Fourier Analysis and Applications, vol.73, issue.10, pp.629-654, 2008. ,
DOI : 10.1007/s00041-008-9035-z
Iterative hard thresholding for compressed sensing, Applied and Computational Harmonic Analysis, vol.27, issue.3, pp.265-274, 2009. ,
DOI : 10.1016/j.acha.2009.04.002
Alternating proximal algorithm for blind image recovery, 2010 IEEE International Conference on Image Processing, 2010. ,
DOI : 10.1109/ICIP.2010.5652173
URL : https://hal.archives-ouvertes.fr/hal-00844115
The ??ojasiewicz Inequality for Nonsmooth Subanalytic Functions with Applications to Subgradient Dynamical Systems, SIAM Journal on Optimization, vol.17, issue.4, pp.1205-1223, 2006. ,
DOI : 10.1137/050644641
A nonsmooth Morse???Sard theorem for subanalytic functions, Journal of Mathematical Analysis and Applications, vol.321, issue.2, pp.729-740, 2006. ,
DOI : 10.1016/j.jmaa.2005.07.068
Clarke Subgradients of Stratifiable Functions, SIAM Journal on Optimization, vol.18, issue.2, pp.556-572, 2007. ,
DOI : 10.1137/060670080
Characterizations of ??ojasiewicz inequalities: Subgradient flows, talweg, convexity, Transactions of the American Mathematical Society, vol.362, issue.06, pp.3319-3363, 2010. ,
DOI : 10.1090/S0002-9947-09-05048-X
Minimization of Non-smooth, Non-convex Functionals by Iterative Thresholding, Journal of Optimization Theory and Applications, vol.52, issue.10 ,
DOI : 10.1007/s10957-014-0614-7
Descent methods for composite nondifferentiable optimization problems, Mathematical Programming, pp.260-279, 1985. ,
DOI : 10.1007/BF01584377
Exact Reconstruction of Sparse Signals via Nonconvex Minimization, IEEE Signal Processing Letters, vol.14, issue.10, pp.707-710, 2007. ,
DOI : 10.1109/LSP.2007.898300
Convergence to steady states in asymptotically autonomous semilinear evolution equations, Nonlinear Analysis, pp.1017-1039, 2003. ,
Nonsmooth analysis and control theory, Graduate texts in Mathematics, vol.178, 1998. ,
DOI : 10.1007/978-1-4614-1806-1_69
URL : https://hal.archives-ouvertes.fr/hal-00863298
Quasi-Fejerian analysis of some optimization algorithms, in Inherently Parallel Algorithms in Feasibility and Optimization and Their Applications, pp.115-152, 2001. ,
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 introduction to o-minimal geometry, RAAG Notes, 1999. ,
The method of steepest descent for non-linear minimization problems, Quarterly of Applied Mathematics, vol.2, issue.3, pp.258-261, 1944. ,
DOI : 10.1090/qam/10667
Geometric theory of dynamical systems. An introduction, 1982. ,
Compressed sensing, IEEE Transactions on Information Theory, vol.52, issue.4, pp.1289-1306, 2006. ,
DOI : 10.1109/TIT.2006.871582
URL : https://hal.archives-ouvertes.fr/inria-00369486
Geometric categories and o-minimal structures, Duke Math, J, vol.84, pp.497-540, 1996. ,
Globally convergent block-coordinate techniques for unconstrained optimization, Optimization Methods and Software, pp.587-637, 1999. ,
Computing proximal points of nonconvex functions, Mathematical Programming, vol.14, issue.5, pp.1-2, 2009. ,
DOI : 10.1007/s10107-007-0124-6
Convergence of Solutions of Second-Order Gradient-Like Systems with Analytic Nonlinearities, Journal of Differential Equations, vol.144, issue.2, pp.313-320, 1999. ,
DOI : 10.1006/jdeq.1997.3393
Convergence in gradient-like systems which are asymptotically autonomous and analytic, Nonlinear Anal, pp.675-698, 2001. ,
Inexact Variants of the Proximal Point Algorithm without Monotonicity, SIAM Journal on Optimization, vol.13, issue.4, pp.1894-1097, 2003. ,
DOI : 10.1137/S1052623401399587
About regularity of collections of sets, Set Valued Analysis, pp.187-206, 2006. ,
On gradients of functions definable in o-minimal structures, Annales de l???institut Fourier, vol.48, issue.3, pp.769-783, 1998. ,
DOI : 10.5802/aif.1638
Pointwise convergence of gradient-like systems, Mathematische Nachrichten, vol.16, issue.13-14, pp.13-14, 2007. ,
DOI : 10.1002/mana.200410564
Active Sets, Nonsmoothness, and Sensitivity, SIAM Journal on Optimization, vol.13, issue.3, pp.702-725, 2003. ,
DOI : 10.1137/S1052623401387623
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.20.9452
Alternating Projections on Manifolds, Mathematics of Operations Research, vol.33, issue.1, pp.216-234, 2008. ,
DOI : 10.1287/moor.1070.0291
URL : https://hal.archives-ouvertes.fr/hal-00317157
Local linear convergence for alternating and averaged nonconvex projections., Found, Comput. Math, vol.9, pp.485-513, 2009. ,
A proximal method for composite minimization, Optimization online, 2008. ,
Une propriété topologique des sous-ensembles analytiques réels la géométrie semi-et sous-analytique, LesÉquations Les´LesÉquations aux Dérivées Partielles Editions du centre National de la Recherche Scientifique, pp.87-89, 1963. ,
Maximum principle in the problem of time optimal response with nonsmooth constraints, Journal of Applied Mathematics and Mechanics, vol.40, issue.6, pp.960-969, 1976. ,
DOI : 10.1016/0021-8928(76)90136-2
Variational analysis and generalized differentiation. I. Basic theory, Grundlehren der Mathematischen Wissenschaften, vol.330, 2006. ,
Accelerating the cubic regularization of Newton???s method on convex problems, Mathematical Programming, vol.108, issue.1, pp.159-181, 2008. ,
DOI : 10.1007/s10107-006-0089-x
Interior-point polynomial algorithms in convex programming, SIAM Studies in Applied Mathematics, vol.13, 1994. ,
DOI : 10.1137/1.9781611970791
Iterative solutions of nonlinear equations in several variables, 1970. ,
DOI : 10.1137/1.9780898719468
Local Convergence of the Proximal Point Algorithm and Multiplier Methods Without Monotonicity, Mathematics of Operations Research, vol.27, issue.1, pp.170-191, 2002. ,
DOI : 10.1287/moor.27.1.170.331
Evolution equations for maximal monotone operators: asymptotic analysis in continuous and discrete time, J. Convex Analysis, vol.17, pp.1113-1163, 2010. ,
Local differentiability of distance functions, Transactions of the American Mathematical Society, vol.352, issue.11, pp.5231-5249, 2000. ,
DOI : 10.1090/S0002-9947-00-02550-2
Variational Analysis, Grundlehren der Mathematischen Wissenschaften, vol.317, 1998. ,
DOI : 10.1007/978-3-642-02431-3
Asymptotics for a Class of Non-Linear Evolution Equations, with Applications to Geometric Problems, The Annals of Mathematics, vol.118, issue.3, pp.525-571, 1983. ,
DOI : 10.2307/2006981
A hybrid projection-proximal point algorithm, Journal of Convex Analysis, vol.6, issue.1, pp.59-70, 1999. ,
A hybrid approximate extragradient-proximal point algorithm using the enlargement of a maximal monotone operator, Set-Valued Analysis, pp.323-345, 1999. ,
A unified framework for some inexact proximal point algorithms , Numerical Functional Analysis and Optimization, pp.1013-1035, 2001. ,
Identifiable Surfaces in Constrained Optimization, SIAM Journal on Control and Optimization, vol.31, issue.4, pp.31-1063, 1993. ,
DOI : 10.1137/0331048
Accelerated block-coordinate relaxation for regularized optimization, Optimization online, 2010. ,
DOI : 10.1137/100808563
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.307.8567