N. J. Balmforth, I. A. Frigaard, and G. Ovarlez, Yielding to Stress: Recent Developments in Viscoplastic Fluid Mechanics, Annual Review of Fluid Mechanics, vol.46, issue.1, pp.121-146, 2014.
DOI : 10.1146/annurev-fluid-010313-141424
URL : https://hal.archives-ouvertes.fr/hal-00973814

P. Coussot, Bingham???s heritage, Rheologica Acta, vol.199, issue.3, pp.163-176, 2016.
DOI : 10.1016/j.cma.2010.06.020

M. Bercovier and M. Engelman, A finite-element method for incompressible non-Newtonian flows, Journal of Computational Physics, vol.36, issue.3, pp.313-326, 1980.
DOI : 10.1016/0021-9991(80)90163-1

T. C. Papanastasiou, Flows of Materials with Yield, Journal of Rheology, vol.31, issue.5, 1987.
DOI : 10.1122/1.549926

M. Fortin and R. Glowinski, Méthodes de lagrangien augmenté: applicationsàapplicationsà la résolution numérique de probì emes aux limites, 1982.

R. Glowinski and P. L. Tallec, Augmented Lagrangian and operator-splitting methods in nonlinear mechanics , SIAM, 1989.
DOI : 10.1137/1.9781611970838

P. Saramito and N. Roquet, An adaptive finite element method for viscoplastic fluid flows in pipes, Computer Methods in Applied Mechanics and Engineering, vol.190, issue.40-41, pp.5391-5412, 2001.
DOI : 10.1016/S0045-7825(01)00175-X

E. J. Dean, R. Glowinski, and G. Guidoboni, On the numerical simulation of Bingham visco-plastic flow: Old and new results, Journal of Non-Newtonian Fluid Mechanics, vol.142, issue.1-3, pp.36-62, 2007.
DOI : 10.1016/j.jnnfm.2006.09.002

R. Glowinski and A. Wachs, On the numerical simulation of viscoplastic fluid flow, Handbook of numerical analysis, pp.483-718, 2011.

T. Treskatis, M. A. Moyers-gonzález, and C. J. Price, An accelerated dual proximal gradient method for applications in viscoplasticity, Journal of Non-Newtonian Fluid Mechanics, vol.238, pp.115-130, 2016.
DOI : 10.1016/j.jnnfm.2016.09.004

P. Saramito and A. Wachs, Progress in numerical simulation of yield stress fluid flows, Rheologica Acta, vol.105, issue.2, pp.1-20, 2017.
DOI : 10.1016/S0377-0257(02)00025-3
URL : https://hal.archives-ouvertes.fr/hal-01375720

J. Bleyer, M. Maillard, P. De-buhan, and P. Coussot, Efficient numerical computations of yield stress fluid flows using second-order cone programming, Computer Methods in Applied Mechanics and Engineering, vol.283, pp.599-614, 2015.
DOI : 10.1016/j.cma.2014.10.008
URL : https://hal.archives-ouvertes.fr/hal-01081508

A. Friaâ, Le matériau de Norton-Hoff généralisé et ses applications en analyse limite, Comptes Rendus de l'Académie des Sciences, Paris Série AB, vol.286, pp.953-956, 1978.

T. Guennouni and P. L. Tallec, Calcuì a la rupture, régularisation de Norton-Hoff et Lagrangien augmenté, Journal de Mécanique Théorique et Appliquée, vol.2, pp.75-99, 1982.

M. Vicente-da-silva and A. Antao, A non-linear programming method approach for upper bound limit analysis, International Journal for Numerical Methods in Engineering, vol.63, issue.10, pp.1192-1218, 2007.
DOI : 10.1137/1.9781611970838

G. Carlier, M. Comte, I. Ionescu, and G. Peyré, A PROJECTION APPROACH TO THE NUMERICAL ANALYSIS OF LIMIT LOAD PROBLEMS, Mathematical Models and Methods in Applied Sciences, vol.75, issue.06, pp.1291-1316, 2011.
DOI : 10.1137/070696143
URL : https://hal.archives-ouvertes.fr/hal-00450000

S. J. Wright, Primal-dual interior-point methods, Siam, 1997.
DOI : 10.1137/1.9781611971453
URL : http://www.cs.wisc.edu/~swright/papers/potra-wright.ps

K. D. Andersen, E. Christiansen, and M. L. Overton, Computing Limit Loads by Minimizing a Sum of Norms, SIAM Journal on Scientific Computing, vol.19, issue.3, pp.1046-1062, 1998.
DOI : 10.1137/S1064827594275303

A. V. Lyamin and S. W. Sloan, Upper bound limit analysis using linear finite elements and non-linear programming, International Journal for Numerical and Analytical Methods in Geomechanics, vol.32, issue.2, pp.181-216, 2002.
DOI : 10.1680/geot.1982.32.3.261

K. Krabbenhoft and L. Damkilde, A general non-linear optimization algorithm for lower bound limit analysis, International Journal for Numerical Methods in Engineering, vol.14, issue.2, pp.165-184, 2003.
DOI : 10.1016/0266-352X(92)90022-L
URL : http://orbit.dtu.dk/en/publications/a-general-nonlinear-optimization-algorithm-for-lower-bound-limit-analysis(a5c4aa67-de22-4c16-ba97-1c99df97dfa8).html

A. Makrodimopoulos and C. Martin, Upper bound limit analysis using simplex strain elements and secondorder cone programming, International journal for numerical and analytical methods in geomechanics, pp.31-835, 2007.

M. S. Lobo, L. Vandenberghe, S. Boyd, and H. Lebret, Applications of second-order cone programming, Linear Algebra and its Applications, vol.284, issue.1-3, pp.193-228, 1998.
DOI : 10.1016/S0024-3795(98)10032-0
URL : https://doi.org/10.1016/s0024-3795(98)10032-0

. Mosek, The Mosek optimization software Available from: http://www.mosek.com URL: Availablefrom:http, 2014.

J. Bleyer, Viscoplastic flows : supplementary code for " advances in the simulation of viscoplastic fluid flows using interior-point methods

T. Goldstein, B. O-'donoghue, S. Setzer, and R. Baraniuk, Fast Alternating Direction Optimization Methods, SIAM Journal on Imaging Sciences, vol.7, issue.3, pp.1588-1623, 2014.
DOI : 10.1137/120896219

Y. Nesterov, A method of solving a convex programming problem with convergence rate o (1/k2), in: Soviet Mathematics Doklady, pp.372-376, 1983.

R. Glowinski, J. Lions, and R. Tremolieres, Numerical analysis of variational inequalities, 2011.

N. Megiddo, Pathways to the Optimal Set in Linear Programming, pp.131-158, 1989.
DOI : 10.1007/978-1-4613-9617-8_8

F. Alizadeh and D. Goldfarb, Second-order cone programming, Mathematical Programming, vol.95, issue.1, pp.95-98, 2003.
DOI : 10.1007/s10107-002-0339-5
URL : http://rutcor.rutgers.edu/pub/rrr/reports2001/51.ps

S. Mehrotra, On the Implementation of a Primal-Dual Interior Point Method, SIAM Journal on Optimization, vol.2, issue.4, pp.575-601, 1992.
DOI : 10.1137/0802028

E. D. Andersen, C. Roos, and T. Terlaky, On implementing a primal-dual interior-point method for conic quadratic optimization, Mathematical Programming, vol.95, issue.2, pp.95-249, 2003.
DOI : 10.1007/s10107-002-0349-3

A. Logg, K. Mardal, and G. Wells, Automated solution of differential equations by the finite element method: The FEniCS book, 2012.
DOI : 10.1007/978-3-642-23099-8

P. R. Amestoy, A. Guermouche, J. Excellent, and S. Pralet, Hybrid scheduling for the parallel solution of linear systems, Parallel Computing, vol.32, issue.2, pp.32-136, 2006.
DOI : 10.1016/j.parco.2005.07.004
URL : https://hal.archives-ouvertes.fr/inria-00070599

P. R. Amestoy, I. S. Duff, J. L. 'excellent, and J. Koster, A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling, SIAM Journal on Matrix Analysis and Applications, vol.23, issue.1, pp.15-41, 2001.
DOI : 10.1137/S0895479899358194
URL : https://hal.archives-ouvertes.fr/hal-00808293

P. Szabo and O. Hassager, Flow of viscoplastic fluids in eccentric annular geometries, Journal of Non-Newtonian Fluid Mechanics, vol.45, issue.2, pp.149-169, 1992.
DOI : 10.1016/0377-0257(92)85001-D

A. Wachs, Numerical simulation of steady Bingham flow through an eccentric annular cross-section by distributed Lagrange multiplier/fictitious domain and augmented Lagrangian methods, Journal of Non-Newtonian Fluid Mechanics, vol.142, issue.1-3, pp.183-198, 2007.
DOI : 10.1016/j.jnnfm.2006.08.009

I. Frigaard and C. Nouar, On the usage of viscosity regularisation methods for visco-plastic fluid flow computation, Journal of Non-Newtonian Fluid Mechanics, vol.127, issue.1, pp.1-26, 2005.
DOI : 10.1016/j.jnnfm.2005.01.003

A. Putz, I. Frigaard, and D. Martinez, On the lubrication paradox and the use of regularisation methods for lubrication flows, Journal of Non-Newtonian Fluid Mechanics, vol.163, issue.1-3, pp.62-77, 2009.
DOI : 10.1016/j.jnnfm.2009.06.006

A. Syrakos, G. C. Georgiou, and A. N. Alexandrou, Solution of the square lid-driven cavity flow of a Bingham plastic using the finite volume method, Journal of Non-Newtonian Fluid Mechanics, vol.195, pp.19-31, 2013.
DOI : 10.1016/j.jnnfm.2012.12.008

A. Aposporidis, P. S. Vassilevski, and A. Veneziani, Multigrid preconditioning of the non-regularized augmented Bingham fluid problem, Electronic Transactions on Numerical Analysis, vol.41, pp.42-61, 2014.

P. Saramito, A damped Newton algorithm for computing viscoplastic fluid flows, Journal of Non-Newtonian Fluid Mechanics, vol.238, pp.6-15, 2016.
DOI : 10.1016/j.jnnfm.2016.05.007
URL : https://hal.archives-ouvertes.fr/hal-01228347

E. A. Yildirim and S. J. Wright, Warm-Start Strategies in Interior-Point Methods for Linear Programming, SIAM Journal on Optimization, vol.12, issue.3, pp.782-810, 2002.
DOI : 10.1137/S1052623400369235
URL : http://www.cs.wisc.edu/~swright/papers/P799.pdf

J. Gondzio and A. Grothey, Reoptimization With the Primal-Dual Interior Point Method, SIAM Journal on Optimization, vol.13, issue.3, pp.842-864, 2002.
DOI : 10.1137/S1052623401393141
URL : http://www.maths.ed.ac.uk/~gondzio/reports/crash.ps

E. John and E. A. Y?ld?r?m, Implementation of warm-start strategies in??interior-point methods for linear programming in??fixed dimension, Computational Optimization and Applications, vol.12, issue.3, pp.151-183, 2008.
DOI : 10.1137/1.9781611971453

N. Roquet and P. Saramito, An adaptive finite element method for Bingham fluid flows around a cylinder, Computer Methods in Applied Mechanics and Engineering, vol.192, issue.31-32, pp.3317-3341, 2003.
DOI : 10.1016/S0045-7825(03)00262-7

S. Boyd and L. Vandenberghe, Convex optimization, 2004.

X. Xu, P. Hung, and Y. Ye, A simplified homogeneous and self-dual linear programming algorithm and its implementation, Annals of Operations Research, vol.19, issue.1, pp.151-171, 1996.
DOI : 10.1007/BF02206815
URL : http://www.stanford.edu/~yyye/yyye/xhy.ps

Y. E. Nesterov and M. J. Todd, Self-Scaled Barriers and Interior-Point Methods for Convex Programming, Mathematics of Operations Research, vol.22, issue.1, pp.1-42, 1997.
DOI : 10.1287/moor.22.1.1
URL : http://ecommons.cornell.edu/bitstream/1813/8975/1/TR001091.pdf

H. Yamashita and H. Yabe, A primal???dual interior point method for nonlinear optimization over second-order cones, Optimization Methods and Software, vol.24, issue.3, pp.407-426, 2009.
DOI : 10.1080/10556780902752447