Abstract
We study optimal control problems with vector-valued controls. In the article, we propose a solution strategy to solve optimal control problems with pointwise convex control constraints. It involves a SQP-like step with an imbedded active-set algorithm.
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J.-P Aubin and H. Frankowska. Set-valued analysis. Birkhäuser, 1990.
J. F. Bonnans. Second-order analysis for constrained optimal control problems of semi-linear elliptic equations. Appl. Math. Optim., 38:303–325, 1998.
J. C. Dunn. Second-order optimality conditions in sets of L ∞ functions with range in a polyhedron. S1AM J. Control Optim., 33(5): 1603–1635, 1995.
M. Hintermüller, K. Ito, and K. Kunisch. The primal-dual active set strategy as a semis-mooth Newton method. SIAM J. Optim., 13:865–888, 2003.
M. Hinze. Optimal and instantaneous control of the instationary Navier-Stokes equations. Habilitation, TU Berlin, 2002.
K. Kunisch and A. Rösch. Primal-dual active set strategy for a general class of constrained optimal control problems. SIAM J. Optim., 13:321–334, 2002.
Zs. Páles and V. Zeidan. Optimum problems with measurable set-valued constraints. SIAMJ. Optim., 11:426–443, 2000.
R. Temam. Navier-Stokes equations. North Holland, Amsterdam, 1979.
F. Tröltzsch. On the Lagrange-Newton-SQP method for the optimal control of semilinear parabolic equations. SIAM J. Control Optim., 38:294–312, 1999.
F. Tröltzsch and D. Wachsmuth. Second-order sufficient optimality conditions for the optimal control of Navier-Stokes equations. ESAIM: COCV, 12:93–119, 2006.
M. Ulbrich. Constrained optimal control of Navier-Stokes flow by semismooth Newton methods. Systems & Control Letters, 48:297–311, 2003.
D. Wachsmuth. Regularity and stability of optimal controls of instationary Navier-Stokes equations. Control and Cybernetics, 34:387–410, 2005.
D. Wachsmuth. Optimal control problems with convex control constraints. Preprint 35-2005, Institut für Mathematik, TU Berlin, submitted, 2005.
D. Wachsmuth. Sufficient second-order optimality conditions for convex control constraints. J. Math. Anal App., 2006. To appear.
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Wachsmuth, D. (2006). Numerical Solution of Optimal Control Problems with Convex Control Constraints. In: Ceragioli, F., Dontchev, A., Furuta, H., Marti, K., Pandolfi, L. (eds) Systems, Control, Modeling and Optimization. CSMO 2005. IFIP International Federation for Information Processing, vol 202. Springer, Boston, MA . https://doi.org/10.1007/0-387-33882-9_30
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DOI: https://doi.org/10.1007/0-387-33882-9_30
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-33881-1
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