A. Alla and . Falcone, A time-adaptive pod method for optimal control problems, Proceedings of the 1st

, IFAC Workshop on Control of Systems Modeled by Partial Differential Equations, p.456, 2013.

A. Alla and M. Falcone, An adaptive pod approximation method for the control of advection-457 diffusion equations, Control and Optimization with PDE Constraints, p.458, 2013.

E. Arian, M. Fahl, and E. Sachs, Trust-region proper orthogonal decomposition for flow 459 control, DTIC Document, 2000.

K. Jerzy, S. Baksalary, and . Puntanen, Generalized matrix versions of the cauchy-schwarz and kantorovich 461 inequalities, Aequationes Mathematicae, vol.41, issue.1, pp.103-110, 1991.

R. E. Bank, B. D. Welfert, and H. Yserentant, A class of iterative methods for solving saddle 463 point problems, Numer. Math, vol.56, issue.7, pp.645-666, 1990.

J. Barzilai and J. M. Borwein, Two-point step size gradient methods, IMA Journal of Numer-465 ical Analysis, vol.8, issue.1, pp.141-148, 1988.

B. Faker, S. Belgacem, and . Kaber, On the Dirichlet boundary controllability of the one-467 dimensional heat equation: semi-analytical calculations and ill-posedness degree, Inverse Problems, vol.19, issue.5, p.55012, 2011.

P. Bjorstad and W. Gropp, Domain decomposition: parallel multilevel methods for elliptic partial 470 differential equations, 2004.

A. Borzì, K. Ito, and K. Kunisch, An optimal control approach to optical flow computation, Internat. J

, ICFD Conference on Numerical Methods for Fluid Dynamics 473, vol.40, pp.231-240, 2001.

H. Richard, G. Byrd, J. Lopez-calva, and . Nocedal, A line search exact penalty method using steering 475 rules, Math. Program, vol.133, issue.1-2, pp.39-73, 2012.

C. Carthel, R. Glowinski, and J. Lions, On exact and approximate boundary controllabilities for the heat 477 equation: a numerical approach, J. Optim. Theory Appl, vol.82, issue.3, pp.429-484, 1994.

A. Cauchy, Méthode générale pour la résolution des systèmes d'équations simultanées, Sciences XXV, S'erie A, issue.25, pp.536-538, 1847.

H. Choi, M. Hinze, and K. Kunisch, Instantaneous control of backward-facing step flows

, Numer. Math, vol.31, issue.2, pp.133-158, 1999.

H. Choi, R. Temam, P. Moin, and J. Kim, Feedback control for unsteady flow and its 483 application to the stochastic Burgers equation, J. Fluid Mech, vol.253, pp.509-543, 1993.

P. G. Ciarlet, Introductionà l'analyse numérique matricielle età l'optimisation, Collection, vol.485

, Mathématiques Appliquées pour la Maîtrise

P. Masson, , 1982.

J. Coron and E. Trélat, Global steady-state controllability of one-dimensional semilinear 488 heat equations, SIAM J. Control Optim, vol.43, issue.2, pp.549-569, 2004.

S. Ervedoza and E. Zuazua, The wave equation: Control and numerics, Control of Partial, p.490
URL : https://hal.archives-ouvertes.fr/hal-00991988

, Differential Equations, p.491, 2012.

J. David and . Evans, Preconditioning Methods: Theory and Applications, 1983.

H. O. Fattorini, Infinite-dimensional optimization and control theory, of Encyclopedia of Mathe-494 matics and its Applications, vol.62, 1999.

W. R. Graham, J. Peraire, and K. Y. Tang, Optimal control of vortex shedding using low-order models. I

, Open-loop model development, Internat. J. Numer. Methods Engrg, vol.44, issue.7, pp.945-972, 1999.

W. R. Graham, J. Peraire, and K. Y. Tang, Optimal control of vortex shedding using low-order models

, Model-based control. Internat. J. Numer. Methods Engrg, vol.44, issue.7, pp.973-990, 1999.

L. Grippo, F. Lampariello, and S. Lucidi, A nonmonotone line search technique for newton's 500 method, SIAM Journal on Numerical Analysis, vol.23, issue.4, pp.707-716, 1986.

J. Marcus, T. Grote, and . Huckle, Parallel preconditioning with sparse approximate inverses, SIAM Jour-502 nal on Scientific Computing, vol.18, pp.838-853, 1997.

M. Gubisch and S. Volkwein, POD a-posteriori error analysis for optimal control problems with 504 mixed control-state constraints, Comput. Optim. Appl, vol.58, issue.3, pp.619-644, 2014.

M. Heinkenschloss, A time-domain decomposition iterative method for the solution of distributed linear 506 quadratic optimal control problems, J. Comput. Appl. Math, vol.173, issue.1, pp.169-198, 2005.

M. Hinze and . Kunisch, Suboptimal control strategies for backward facing step ows, Proceedings of 15th

, IMACS World Congress on Scientific Computation, Modelling and Applied Mathematics, vol.3, pp.53-58, 1997.

M. Hinze, Optimal and instantaneous control of the instationary navier-stokes equations, p.511, 2000.

M. Hinze and K. Kunisch, Three control methods for time-dependent fluid flow. Flow Turbul. Com-512 bust, vol.65, pp.273-298, 2000.

K. Ito and S. S. Ravindran, A reduced basis method for control problems governed by PDEs, Control 514 and estimation of distributed parameter systems, vol.126, pp.153-168, 1996.

K. Ito and S. S. Ravindran, Reduced basis method for optimal control of unsteady viscous flows, Int. J

, Comput. Fluid Dyn, vol.15, issue.2, pp.97-113, 2001.

L. V. Kantorovich, Functional analysis and applied mathematics, p.519

K. Kunisch, S. Volkwein, and L. Xie, HJB-POD-based feedback design for the optimal control of evolution 521 problems, SIAM J. Appl. Dyn. Syst, vol.3, issue.4, pp.701-722, 2004.

J. E. Lagnese and G. Leugering, Time-domain decomposition of optimal control problems for the wave 523 equation, Systems Control Lett, vol.48, issue.3-4, p.524, 2003.

I. Lasiecka and R. Triggiani, Control theory for partial differential equations: continuous and ap-525 proximation theories. I-II, 75 of Encyclopedia of Mathematics and its Applications. Cambridge, vol.47

, Abstract hyperbolic-like systems over a finite time horizon, 2000.

C. Lee, J. Kim, and H. Choi, Suboptimal control of turbulent channel flow for drag 528 reduction, Journal of Fluid Mechanics, vol.358, pp.245-258, 1998.

J. Lions, Y. Maday, and G. Turinici, A"parareal"in time discretization of pde's. Comptes Rendus de 530 l, Academie des Sciences Series I Mathematics, vol.332, issue.7, pp.661-668, 2001.

J. Lions, Optimal control of systems governed by partial differential equations, p.532

S. K. Mitter, Die Grundlehren der mathematischen Wissenschaften, vol.170, 1971.

J. Lions, Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués, Recherches en Mathématiques Appliquées, vol.535, issue.2, pp.8-9

P. Masson, , 1988.

, Contrôlabilité exacte

Y. Maday, J. Salomon, and G. Turinici, Monotonic parareal control for quantum systems, SIAM Journal on 539 Numerical Analysis, vol.45, issue.6, pp.2468-2482, 2007.

Y. Maday, M. Riahi, and J. Salomon, Parareal in time intermediate targets methods 541 for optimal control problems, Control and Optimization with PDE Constraints, vol.542

, Mathematics, pp.79-92, 2013.

Y. Maday and G. Turinici, A parareal in time procedure for the control of partial differential equa-545 tions, C. R. Math. Acad. Sci, vol.335, issue.4, pp.387-392, 2002.

T. Malas and L. Gürel, Incomplete lu preconditioning with the multilevel fast multipole algorithm 547 for electromagnetic scattering, SIAM Journal on Scientific Computing, vol.29, issue.4, p.548, 2007.

X. Marduel and K. Kunisch, Suboptimal control of transient nonisothermal viscoelastic fluid flows. 549 Physics of Fluids (1994-present), vol.13, pp.2478-2491, 2001.

S. Micu and E. Zuazua, Regularity issues for the null-controllability of the linear 1-d heat equation

, Systems Control Lett, vol.60, issue.6, pp.406-413, 2011.

O. Pironneau, F. Hecht, and J. Morice, , 2013.

A. Quarteroni and A. Valli, Domain decomposition methods for partial differential equations, Nu, p.554

, merical Mathematics and Scientific Computation. The Clarendon Press, vol.555, 1999.

. Ss-ravindran, Proper orthogonal decomposition in optimal control of fluids, vol.99, 1999.

T. Rees, M. Stoll, and A. Wathen, All-at-once preconditioning in PDE-constrained optimization

, Kybernetika (Prague), vol.46, issue.2, pp.341-360, 2010.

U. Rüde, Mathematical and computational techniques for multilevel adaptive methods, SIAM, p.561, 1993.

Y. Saad, Iterative methods for sparse linear systems, 2003.

S. Enterprises, Scilab: Le logiciel open source gratuit de calcul numrique, Scilab Enterprises, p.563

. France, , 2012.

D. Silvester and A. Wathen, Fast iterative solution of stabilised Stokes systems. II. Using general 565 block preconditioners, SIAM J. Numer. Anal, vol.31, issue.5, pp.1352-1367, 1994.

M. Stoll and A. Wathen, All-at-once solution of time-dependent Stokes control, J. Comput. Phys, vol.567, pp.498-515, 2013.

A. Toselli and O. Widlund, Domain decomposition methods: algorithms and theory, vol.3

. Springer, , 2005.

F. Tröltzsch, Optimal control of partial differential equations, Graduate Studies in Mathe, vol.112, p.571

, Theory, methods and applications, Translated 572 from the 2005 German original by Jürgen Sprekels, 2010.

S. Ulbrich, Generalized sqp-methods with ?parareal? time-domain decomposition for time-dependent 574

, Real-time PDE-constrained optimization, vol.3, pp.145-168, 2007.

A. Wathen and D. Silvester, Fast iterative solution of stabilised Stokes systems. I. Using simple 577 diagonal preconditioners, SIAM J. Numer. Anal, vol.30, issue.3, pp.630-649, 1993.

G. Yuan and Z. Wei, The Barzilai and Borwein gradient method with nonmonotone line search 579 for nonsmooth convex optimization problems, Math. Model. Anal, vol.17, issue.2, pp.203-216, 2012.