Convergence of an SQP-Method for a Class of Nonlinear Parabolic Boundary Control Problems

  • Fredi Tröltzsch
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 118)


We investigate local convergence of an SQP method for an optimal control problem governed by a parabolic equation with nonlinear boundary condition. Sufficient conditions for local quadratic convergence of the method are discussed.

1991 Mathematics Subject Classification

49M05 49M40 49K24 

Key words and phrases

Sequential quadratic programming optimal control parabolic equation nonlinear boundary condition control constraints 


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  1. 1.
    Alt, W.: The Lagrange-Newton method for infinite-dimensional optimization problems. Numer. Funct. Anal. and Optimization 11 (1990), 201–224.MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Alt, W.: Sequential quadratic programming in Banach spaces. In W. Oettli and D. Pallaschke, editors, Advances in Optimization, number 382 in Lecture Notes in Economics and Mathematical Systems, 281–301. Springer Verlag, 1992.Google Scholar
  3. 3.
    Alt, W. and K. Malanowski: The Lagrange-Newton method for nonlinear optimal control problems. Computational Optimization and Applications, 2 (1993), 77–100.MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Alt,W., Sontag, R., and F. Tröltzsch: An SQP method for optimal control of weakly singular Hammerstein integral equations. DFG-Schwerpunktprogramm “Anwendungsbezogene Optimierung und Steuerung ”, Report No. 423 (1993), to appear in Appl. Math. Optimization.Google Scholar
  5. 5.
    Amann, H.: Parabolic evolution equations with nonlinear boundary conditions. In F.E. Browder, editor, Nonlinear Functional Analysis Proc. Sympos. Pure Math., Vol. 45, Part I, 17–27, 1986.Google Scholar
  6. 6.
    Goldberg, H. and F. Tröltzsch: Second order optimality conditions for nonlinear parabolic boundary control problems. SIAM J. Contr. Opt. 31 (1993), 1007–1025.zbMATHCrossRefGoogle Scholar
  7. 7.
    Kelley, C.T. and S.J. Wright: Sequential quadratic programming for certain parameter identification problems. Math. Programming 51 (1991) , 281–305.MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Kupfer, S.-F. and Sachs, E.W.: Numerical solution of a nonlinear parabolic control problem by a reduced sqp method. Computational Optimization and Applications 1 (1992), 113–135.MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Krasnoselski, M.A. et al.: Linear operators in spaces of summable functions (in Russian). Nauka, Moscow, 1966.Google Scholar
  10. 10.
    Levitin, E.S. and B.T. Polyak: Constrained minimization methods. USSR J. Comput. Math. and Math. Phys. 6 (1966), 1–50.CrossRefGoogle Scholar
  11. 11.
    Tröltzsch, F.: On the semigroup approach for the optimal control of semilinear parabolic equations including distributed an boundary control. Z. für Analysis und Anwendungen 8 (1989), 431–443.zbMATHGoogle Scholar
  12. 12.
    Tröltzsch, F.: An SQP Method for Optimal Control of a Nonlinear Heat Equation (1993), to appear in Control Cybernetics.Google Scholar

Copyright information

© Springer Basel AG 1994

Authors and Affiliations

  • Fredi Tröltzsch
    • 1
  1. 1.Department of MathematicsTechnical University of Chemnitz-ZwickauChemnitzGermany

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