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All issues Volume 48 / No 6 (November-December 2014) ESAIM: M2AN, 48 6 (2014) 1615-1638 References
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Issue
ESAIM: M2AN
Volume 48, Number 6, November-December 2014
Page(s) 1615 - 1638
DOI https://doi.org/10.1051/m2an/2014012
Published online 09 September 2014
  1. N. Altmüller and L. Grüne, Distributed and boundary model predictive control for the heat equation. GAMM Mitteilungen 35 (2012) 131–145. [CrossRef] [MathSciNet] [Google Scholar]
  2. A.C. Antoulas, Approximation of Large-Scale Dynamical Systems. Advances in Design and Control. SIAM (2005). [Google Scholar]
  3. J.A. Atwell and B.B. King, Proper orthogonal decomposition for reduced basis feedback controllers for parabolic equations. Math. Comput. Model. 33 (2001) 1–19. [CrossRef] [Google Scholar]
  4. R. Becker, H. Kapp and R. Rannacher, Adaptive finite element methods for optimal control of partial differential equations: Basic concept. SIAM J. Control Optim. 39 (2000) 113–132. [Google Scholar]
  5. P. Benner, V. Mehrmann and D. Sorensen, Dimension reduction of large-scale systems, vol. 45 of Lect. Notes Computational Science and Engineering. Berlin, Springer (2005). [Google Scholar]
  6. L. Dedè, Reduced basis method and a posteriori error estimation for parametrized linear-quadratic optimal control problems. SIAM J. Sci. Comput. 32 (2010) 997–1019. [CrossRef] [Google Scholar]
  7. L. Dedè, Reduced basis method and error estimation for parametrized optimal control problems with control constraints. J. Sci. Comput. 50 (2012) 287–305. [CrossRef] [Google Scholar]
  8. J. Eftang, D. Huynh, D. Knezevic and A. Patera, A two-step certified reduced basis method. J. Sci. Comput. 51 (2012) 28–58. [CrossRef] [Google Scholar]
  9. A.-L. Gerner and K. Veroy, Certified reduced basis methods for parametrized saddle point problems. SIAM J. Sci. Comput. 34 (2012) A2812–A2836. [CrossRef] [Google Scholar]
  10. M.A. Grepl and M. Kärcher, Reduced basis a posteriori error bounds for parametrized linear-quadratic elliptic optimal control problems. C.R. Math. 349 (2011) 873–877. [CrossRef] [Google Scholar]
  11. M.A. Grepl and A.T. Patera, A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations. ESAIM: M2AN 39 (2005) 157–181. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  12. M. Gunzburger and A. Kunoth, Space-time adaptive wavelet methods for optimal control problems constrained by parabolic evolution equations. SIAM J. Control Optim. (2011) 1150–1170. [Google Scholar]
  13. B. Haasdonk and M. Ohlberger, Reduced basis method for finite volume approximations of parametrized linear evolution equations. ESAIM: M2AN 42 (2008) 277–302. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  14. W. Hager, Multiplier methods for nonlinear optimal control. SIAM J. Numer. Anal. 27 (1990) 1061–1080. [CrossRef] [Google Scholar]
  15. M. Hinze, R. Pinnau, M. Ulbrich and S. Ulbrich, Optimization with PDE Constraints, vol. 23 of Math. Model. Theor. Appl. Springer (2009). [Google Scholar]
  16. D.B.P. Huynh, G. Rozza, S. Sen and A.T. Patera, A successive constraint linear optimization method for lower bounds of parametric coercivity and inf-sup stability constants. C.R. Math. 345 (2007) 473–478. [Google Scholar]
  17. L. Iapichino, S. Ulbrich and S. Volkwein. Multiobjective PDE-constrained optimization using the reduced-basis method. Technical report, Universität Konstanz (2013). [Google Scholar]
  18. K. Ito and K. Kunisch, Receding horizon optimal control for infinite dimensional systems. ESAIM: COCV 8 (2002) 741–760. [CrossRef] [EDP Sciences] [Google Scholar]
  19. K. Ito and K. Kunisch, Reduced-order optimal control based on approximate inertial manifolds for nonlinear dynamical systems. SIAM J. Numer. Anal. 46 (2008) 2867–2891. [CrossRef] [Google Scholar]
  20. K. Ito and S.S. Ravindran, A reduced-order method for simulation and control of fluid flows. J. Comput. Phys. 143 (1998) 403–425. [CrossRef] [MathSciNet] [Google Scholar]
  21. K. Ito and S.S. Ravindran, A reduced basis method for optimal control of unsteady viscous flows. Int. J. Comput. Fluid D. 15 (2001) 97–113. [CrossRef] [MathSciNet] [Google Scholar]
  22. M. Kärcher, The reduced-basis method for parametrized linear-quadratic elliptic optimal control problems. Master’s thesis, Technische Universität München (2011). [Google Scholar]
  23. M. Kärcher and M.A. Grepl. A certified reduced basis method for parametrized elliptic optimal control problems. ESAIM: COCV 20 (2014) 416–441. [CrossRef] [EDP Sciences] [Google Scholar]
  24. K. Kunisch and S. Volkwein, Control of the Burgers equation by a reduced-order approach using proper orthogonal decomposition. J. Optim. Theory Appl. 102 (1999) 345–371. [CrossRef] [MathSciNet] [Google Scholar]
  25. K. Kunisch, S. Volkwein and L. Xie, HJB-POD based feedback design for the optimal control of evolution problems. SIAM J. Appl. Dyn. Syst. 3 (2004) 701–722. [Google Scholar]
  26. G. Leugering, S. Engell, A. Griewank, M. Hinze, R. Rannacher, V. Schulz, M. Ulbrich and S. Ulbrich, Constrained Optimization and Optimal Control for Partial Differential Equations. International Series of Numerical Mathematics. Birkhäuser Basel (2012). [Google Scholar]
  27. J.L. Lions, Optimal Control of Systems Governed by Partial Differential Equations. Springer (1971). [Google Scholar]
  28. K. Malanowski, C. Buskens and H. Maurer, Convergence of approximations to nonlinear optimal control problems, vol. 195. CRC Press (1997) 253–284. [Google Scholar]
  29. F. Negri, G. Rozza, A. Manzoni and A. Quarteroni, Reduced basis method for parametrized elliptic optimal control problems. SIAM J. Sci. Comput. 35 (2013) A2316–A2340. [Google Scholar]
  30. I. B. Oliveira, A “HUM” Conjugate Gradient Algorithm for Constrained Nonlinear Optimal Control: Terminal and Regulator Problems. Ph.D. thesis, Massachusetts Institute of Technology (2002). [Google Scholar]
  31. C. Prud’homme, D.V. Rovas, K. Veroy, L. Machiels, Y. Maday, A.T. Patera and G. Turinici. Reliable real-time solution of parametrized partial differential equations: Reduced-basis output bound methods. J. Fluid. Eng. 124 (2002) 70–80. [Google Scholar]
  32. A.M. Quarteroni and A. Valli, Numerical Approximation of Partial Differential Equations, vol. 23 of Springer Ser. Comput. Math. Springer (2008). [Google Scholar]
  33. G. Rozza, D.B.P. Huynh and A.T. Patera, Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Arch. Comput. Method. E. 15 (2008) 229–275. [Google Scholar]
  34. G. Rozza and K. Veroy, On the stability of the reduced basis method for Stokes equations in parametrized domains. Comput. Methods Appl. Mech. Engrg. 196 (2007) 1244–1260. [Google Scholar]
  35. T. Tonn, K. Urban and S. Volkwein, Comparison of the reduced-basis and pod a posteriori error estimators for an elliptic linear-quadratic optimal control problem. Math. Comput. Model. Dyn. 17 (2011) 355–369. [CrossRef] [MathSciNet] [Google Scholar]
  36. F. Tröltzsch and S. Volkwein, POD a-posteriori error estimates for linear-quadratic optimal control problems. Comput. Optim. Appl. 44 (2009) 83–115. [CrossRef] [Google Scholar]
  37. K. Urban and A.T. Patera, A new error bound for reduced basis approximation of parabolic partial differential equations. C. R. Math. 350 (2012) 203–207. [Google Scholar]
  38. K. Veroy, D.V. Rovas and A.T. Patera, A posteriori error estimation for reduced-basis approximation of parametrized elliptic coercive partial differential equations: “convex inverse” bound conditioners. Special Volume: A tribute to J.L. Lions. ESAIM: COCV 8 (2002) 1007–1028. [CrossRef] [EDP Sciences] [Google Scholar]

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