Abstract
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.
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References
Alt, W.: The Lagrange-Newton method for infinite-dimensional optimization problems. Numer. Funct. Anal. and Optimization 11 (1990), 201–224.
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.
Alt, W. and K. Malanowski: The Lagrange-Newton method for nonlinear optimal control problems. Computational Optimization and Applications, 2 (1993), 77–100.
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.
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.
Goldberg, H. and F. Tröltzsch: Second order optimality conditions for nonlinear parabolic boundary control problems. SIAM J. Contr. Opt. 31 (1993), 1007–1025.
Kelley, C.T. and S.J. Wright: Sequential quadratic programming for certain parameter identification problems. Math. Programming 51 (1991) , 281–305.
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.
Krasnoselski, M.A. et al.: Linear operators in spaces of summable functions (in Russian). Nauka, Moscow, 1966.
Levitin, E.S. and B.T. Polyak: Constrained minimization methods. USSR J. Comput. Math. and Math. Phys. 6 (1966), 1–50.
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.
Tröltzsch, F.: An SQP Method for Optimal Control of a Nonlinear Heat Equation (1993), to appear in Control Cybernetics.
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Tröltzsch, F. (1994). Convergence of an SQP-Method for a Class of Nonlinear Parabolic Boundary Control Problems. In: Desch, W., Kappel, F., Kunisch, K. (eds) Control and Estimation of Distributed Parameter Systems: Nonlinear Phenomena. ISNM International Series of Numerical Mathematics, vol 118. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8530-0_19
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DOI: https://doi.org/10.1007/978-3-0348-8530-0_19
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9666-5
Online ISBN: 978-3-0348-8530-0
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