P. Absil, R. Mahony, and B. Andrews, 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

A. Aragon, A. Dontchev, and M. Geoffroy, 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

H. Attouch and J. Bolte, 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

H. Attouch, J. Bolte, P. Redont, and A. Soubeyran, 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.

H. Attouch, J. Bolte, P. Redont, and A. Soubeyran, 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

H. Attouch, L. M. Briceño-arias, and P. L. Combettes, 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

H. Attouch and A. Soubeyran, Local search proximal algorithms as decision dynamics with costs to move, Set Valued and Variational Analysis, Online First, p.12, 2010.

A. Auslender, 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. Beck and M. Teboulle, 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.

R. Benedetti and J. Risler, Real Algebraic and Semialgebraic Sets, des Sciences et des Arts, 1990.

T. Blumensath and M. E. Davis, 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

T. Blumensath and M. E. Davis, 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

J. Bolte, P. L. Combettes, and J. Pesquet, 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

J. Bolte, A. Daniilidis, and A. Lewis, 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

J. Bolte, A. Daniilidis, and A. Lewis, 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

J. Bolte, A. Daniilidis, A. Lewis, and M. Shiota, Clarke Subgradients of Stratifiable Functions, SIAM Journal on Optimization, vol.18, issue.2, pp.556-572, 2007.
DOI : 10.1137/060670080

J. Bolte, A. Daniilidis, O. Ley, and L. Mazet, 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

K. Bredies and D. A. Lorenz, 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

J. V. Burke, Descent methods for composite nondifferentiable optimization problems, Mathematical Programming, pp.260-279, 1985.
DOI : 10.1007/BF01584377

R. Chartrand, 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

R. Chill and M. A. Jendoubi, Convergence to steady states in asymptotically autonomous semilinear evolution equations, Nonlinear Analysis, pp.1017-1039, 2003.

F. H. Clarke, Y. Ledyaev, R. I. Stern, and P. R. Wolenski, 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

P. L. Combettes, Quasi-Fejerian analysis of some optimization algorithms, in Inherently Parallel Algorithms in Feasibility and Optimization and Their Applications, pp.115-152, 2001.

P. L. Combettes and V. R. Wajs, 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

M. Coste, An introduction to o-minimal geometry, RAAG Notes, 1999.

H. B. Curry, 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

J. Palis and W. De-melo, Geometric theory of dynamical systems. An introduction, 1982.

D. L. Donoho, 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

L. Miller and C. , Geometric categories and o-minimal structures, Duke Math, J, vol.84, pp.497-540, 1996.

L. Grippo and M. Sciandrone, Globally convergent block-coordinate techniques for unconstrained optimization, Optimization Methods and Software, pp.587-637, 1999.

W. Hare and C. Sagastizábal, Computing proximal points of nonconvex functions, Mathematical Programming, vol.14, issue.5, pp.1-2, 2009.
DOI : 10.1007/s10107-007-0124-6

A. Haraux and M. A. Jendoubi, 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

S. Huang and P. Taka?, Convergence in gradient-like systems which are asymptotically autonomous and analytic, Nonlinear Anal, pp.675-698, 2001.

A. N. Iusem, T. Pennanen, and B. Svaiter, 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

A. Y. Kruger, About regularity of collections of sets, Set Valued Analysis, pp.187-206, 2006.

K. Kurdyka, 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

C. Lageman, Pointwise convergence of gradient-like systems, Mathematische Nachrichten, vol.16, issue.13-14, pp.13-14, 2007.
DOI : 10.1002/mana.200410564

A. S. Lewis, 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

A. S. Lewis and J. Malick, 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

A. S. Lewis, D. R. Luke, and J. Malick, Local linear convergence for alternating and averaged nonconvex projections., Found, Comput. Math, vol.9, pp.485-513, 2009.

A. S. Lewis and S. J. Wright, A proximal method for composite minimization, Optimization online, 2008.

S. Lojasiewicz, 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.

B. Mordukhovich, 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

B. Mordukhovich, Variational analysis and generalized differentiation. I. Basic theory, Grundlehren der Mathematischen Wissenschaften, vol.330, 2006.

Y. Nesterov, 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

Y. Nesterov and A. Nemirovskii, Interior-point polynomial algorithms in convex programming, SIAM Studies in Applied Mathematics, vol.13, 1994.
DOI : 10.1137/1.9781611970791

J. M. Ortega and W. C. Rheinboldt, Iterative solutions of nonlinear equations in several variables, 1970.
DOI : 10.1137/1.9780898719468

T. Pennanen, 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

J. Peypouquet and S. Sorin, Evolution equations for maximal monotone operators: asymptotic analysis in continuous and discrete time, J. Convex Analysis, vol.17, pp.1113-1163, 2010.

R. A. Poliquin, R. T. Rockafellar, and L. Thibault, 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

R. T. Rockafellar and R. Wets, Variational Analysis, Grundlehren der Mathematischen Wissenschaften, vol.317, 1998.
DOI : 10.1007/978-3-642-02431-3

L. Simon, 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

M. V. Solodov and B. F. Svaiter, A hybrid projection-proximal point algorithm, Journal of Convex Analysis, vol.6, issue.1, pp.59-70, 1999.

M. V. Solodov and B. F. Svaiter, A hybrid approximate extragradient-proximal point algorithm using the enlargement of a maximal monotone operator, Set-Valued Analysis, pp.323-345, 1999.

M. V. Solodov and B. F. Svaiter, A unified framework for some inexact proximal point algorithms , Numerical Functional Analysis and Optimization, pp.1013-1035, 2001.

S. J. Wright, Identifiable Surfaces in Constrained Optimization, SIAM Journal on Control and Optimization, vol.31, issue.4, pp.31-1063, 1993.
DOI : 10.1137/0331048

S. J. Wright, 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