Numerical Solution of Optimal Control Problems with Convex Control Constraints

  • D. Wachsmuth
Part of the IFIP International Federation for Information Processing book series (IFIPAICT, volume 202)


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.


Optimal control convex control constraints set-valued mappings 


  1. [1]
    J.-P Aubin and H. Frankowska. Set-valued analysis. Birkhäuser, 1990.Google Scholar
  2. [2]
    J. F. Bonnans. Second-order analysis for constrained optimal control problems of semi-linear elliptic equations. Appl. Math. Optim., 38:303–325, 1998.MATHMathSciNetCrossRefGoogle Scholar
  3. [3]
    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.MATHMathSciNetCrossRefGoogle Scholar
  4. [4]
    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.MATHCrossRefGoogle Scholar
  5. [5]
    M. Hinze. Optimal and instantaneous control of the instationary Navier-Stokes equations. Habilitation, TU Berlin, 2002.Google Scholar
  6. [6]
    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.MATHMathSciNetCrossRefGoogle Scholar
  7. [7]
    Zs. Páles and V. Zeidan. Optimum problems with measurable set-valued constraints. SIAMJ. Optim., 11:426–443, 2000.MATHCrossRefGoogle Scholar
  8. [8]
    R. Temam. Navier-Stokes equations. North Holland, Amsterdam, 1979.Google Scholar
  9. [9]
    F. Tröltzsch. On the Lagrange-Newton-SQP method for the optimal control of semilinear parabolic equations. SIAM J. Control Optim., 38:294–312, 1999.MATHMathSciNetCrossRefGoogle Scholar
  10. [10]
    F. Tröltzsch and D. Wachsmuth. Second-order sufficient optimality conditions for the optimal control of Navier-Stokes equations. ESAIM: COCV, 12:93–119, 2006.CrossRefGoogle Scholar
  11. [11]
    M. Ulbrich. Constrained optimal control of Navier-Stokes flow by semismooth Newton methods. Systems & Control Letters, 48:297–311, 2003.MathSciNetCrossRefGoogle Scholar
  12. [12]
    D. Wachsmuth. Regularity and stability of optimal controls of instationary Navier-Stokes equations. Control and Cybernetics, 34:387–410, 2005.MathSciNetGoogle Scholar
  13. [13]
    D. Wachsmuth. Optimal control problems with convex control constraints. Preprint 35-2005, Institut für Mathematik, TU Berlin, submitted, 2005.Google Scholar
  14. [14]
    D. Wachsmuth. Sufficient second-order optimality conditions for convex control constraints. J. Math. Anal App., 2006. To appear.Google Scholar

Copyright information

© International Federation for Information Processing 2006

Authors and Affiliations

  • D. Wachsmuth
    • 1
  1. 1.Institut für MathematikTU BerlinBerlinGermany

Personalised recommendations