M. S. Alnaes, UFL: a Finite Element Form Language, 2012.

M. S. Alnaes, J. Blechta, J. Hake, A. Johansson, B. Kehlet et al., The FEniCS Project version 1.5. Archive of Numerical Software, p.3, 2015.

M. S. Alnaes, A. Logg, K. B. Ølgaard, M. E. Rognes, and G. N. Wells, Unified Form Language: A domain-specific language for weak formulations of partial differential equations, ACM Transactions on Mathematical Software, issue.2, p.40, 2014.

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.249-277, 2003.

S. Balay, S. Abhyankar, M. F. Adams, J. Brown, P. Brune et al., , 2016.

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, pp.121-146, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00973814

A. Ben-tal, L. El-ghaoui, and A. Nemirovski, Robust optimization, vol.28, 2009.

A. Ben-tal and A. Nemirovski, Lectures on modern convex optimization: analysis, algorithms, and engineering applications, vol.2, 2001.

A. Ben-tal and A. Nemirovski, Robust optimization-methodology and applications, Mathematical Programming, vol.92, issue.3, pp.453-480, 2002.

J. Benamou and Y. Brenier, A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem, Numerische Mathematik, vol.84, issue.3, pp.375-393, 2000.

M. P. Bendsoe and O. Sigmund, Topology Optimization: Theory, Methods and Applications, 2004.

J. Bleyer, Advances in the simulation of viscoplastic fluid flows using interior-point methods, Computer Methods in Applied Mechanics and Engineering, vol.330, pp.368-394, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01672045

J. Bleyer, fenics-optim -Convex optimization interface in FEniCS, 2020.

J. Bleyer, G. Carlier, V. Duval, J. Mirebeau, and G. Peyré, A ?-convergence result for the upper bound limit analysis of plates, ESAIM: Mathematical Modelling and Numerical Analysis, vol.50, issue.1, pp.215-235, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01069919

J. Bleyer and P. De-buhan, On the performance of non-conforming finite elements for the upper bound limit analysis of plates, International Journal for Numerical Methods in Engineering, vol.94, issue.3, pp.308-330, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00776908

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.
URL : https://hal.archives-ouvertes.fr/hal-01081508

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

A. Capsoni and L. Corradi, Limit analysis of plates-a finite element formulation, Structural Engineering and Mechanics, vol.8, issue.4, pp.325-341, 1999.

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.21, issue.06, pp.1291-1316, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00450000

G. Carlier, M. Comte, and G. Peyré, Approximation of maximal cheeger sets by projection, ESAIM: Mathematical Modelling and Numerical Analysis, vol.43, issue.1, pp.139-150, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00359736

A. Chambolle and T. Pock, Crouzeix-Raviart approximation of the total variation on simplicial meshes, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01787012

R. Chares, Cones and interior-point algorithms for structured convex optimization involving powers andexponentials, 2009.

J. Cheeger, A lower bound for the smallest eigenvalue of the Laplacian, Proceedings of the Princeton conference in honor of Professor S. Bochner, 1969.

P. L. Combettes and J. Pesquet, Primal-dual splitting algorithm for solving inclusions with mixtures of composite, lipschitzian, and parallel-sum type monotone operators. Set-Valued and variational analysis, vol.20, pp.307-330, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00794044

L. Condat, A primal-dual splitting method for convex optimization involving Lipschitzian, proximable and linear composite terms, Journal of Optimization Theory and Applications, vol.158, issue.2, pp.460-479, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00609728

P. Coussot, Bingham's heritage, Rheologica Acta, vol.6, issue.3, pp.163-176, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01784850

F. Demengel, Problemes variationnels en plasticité parfaite des plaques, Numerical Functional Analysis and Optimization, vol.6, issue.1, pp.73-119, 1983.

F. Demengel, Fonctions à hessien borné, Annales de l'institut Fourier, vol.34, pp.155-190, 1984.

S. Dumont and N. Igbida, On a dual formulation for the growing sandpile problem, European Journal of Applied Mathematics, vol.20, issue.2, pp.169-185, 2009.
URL : https://hal.archives-ouvertes.fr/hal-01113763

G. Duvaut and J. L. Lions, Inequalities in mechanics and physics, vol.219, 2012.

R. Glowinski, Numerical Methods for Nonlinear Variational Problems, Springer Series in Computational Physics, vol.158, 1984.

Y. Kanno, Nonsmooth mechanics and convex optimization, 2011.

Y. Kanno and X. Guo, A mixed integer programming for robust truss topology optimization with stress constraints, International Journal for Numerical Methods in Engineering, vol.83, issue.13, pp.1675-1699, 2010.

B. Kawohl and M. Novaga, The p-Laplace eigenvalue problem as p? 1 and Cheeger sets in a Finsler metric, Journal of Convex Analysis, vol.15, issue.3, p.623, 2008.

D. Kinderlehrer and G. Stampacchia, An introduction to variational inequalities and their applications, vol.31, 1980.

R. C. Kirby and A. Logg, A compiler for variational forms, ACM Transactions on Mathematical Software, issue.3, p.32, 2006.

M. S. Lobo, L. Vandenberghe, S. Boyd, and H. Lebret, Applications of second-order cone programming. Linear algebra and its applications, vol.284, pp.193-228, 1998.

A. Logg, K. Mardal, and G. Wells, Automated solution of differential equations by the finite element method: The FEniCS book, vol.84, 2012.

A. Logg, K. B. Ølgaard, M. E. Rognes, and G. N. Wells, FFC: the FEniCS Form Compiler, 2012.

A. Logg and G. N. Wells, Dolfin: Automated finite element computing, ACM Transactions on Mathematical Software, vol.37, issue.2, 2010.

A. Logg, G. N. Wells, and J. Hake, DOLFIN: a C++/Python Finite Element Library, chapter 10, 2012.

K. Malanowski, Convergence of approximations vs. regularity of solutions for convex, control-constrained optimal-control problems, Applied Mathematics and Optimization, vol.8, issue.1, pp.69-95, 1982.

Y. Meyer, Oscillating patterns in image processing and nonlinear evolution equations: the fifteenth Dean Jacqueline B. Lewis memorial lectures, vol.22, 2001.

,. Mosek-aps, The MOSEK optimization API for Python 8, 2018.

. Mosek-aps, MOSEK Modeling Cookbook, 2019.

T. Munson, J. Sarich, S. Wild, S. Benson, and L. C. Mcinnes, , 2012.

M. L. Overton, Numerical solution of a model problem from collapse load analysis, Proc. of the sixth int'l. symposium on Computing methods in applied sciences and engineering, pp.421-437, 1985.

N. Papadakis, G. Peyré, and E. Oudet, Optimal transport with proximal splitting, SIAM Journal on Imaging Sciences, vol.7, issue.1, pp.212-238, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00918460

G. Peyré and M. Cuturi, Computational optimal transport. Foundations and Trends in Machine Learning, vol.11, pp.355-607, 2019.

L. Prigozhin, Variational model of sandpile growth, European Journal of Applied Mathematics, vol.7, issue.3, pp.225-235, 1996.

G. Strang, A minimax problem in plasticity theory, Functional analysis methods in numerical analysis, pp.319-333, 1979.

R. Trémolières, J. Lions, and R. Glowinski, Numerical analysis of variational inequalities, vol.8, 2011.

C. Villani, Topics in optimal transportation, Number, vol.58, 2003.

P. Weiss, L. Blanc-féraud, A. , and G. , Efficient schemes for total variation minimization under constraints in image processing, SIAM journal on Scientific Computing, vol.31, issue.3, pp.2047-2080, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00166096

K. Yonekura and Y. Kanno, Global optimization of robust truss topology via mixed integer semidefinite programming, Optimization and Engineering, vol.11, issue.3, pp.355-379, 2010.