Abstract
We investigate local convergence of the Lagrange-Newton method for nonlinear optimal control problems subject to control constraints including the situation where the terminal state is fixed. Sufficient conditions for local quadratic convergence of the method based on stability results for the solutions of nonlinear control problems are discussed.
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References
W. Alt, “The Lagrange-Newton method for infinite-dimensional optimization problems,”Numer. Funct. Anal. and Optimiz. 11 (1990), 201–224.
W. Alt, “Parametric programming with applications to optimal control and sequential quadratic programming,”Bayreuther Mathematische Schriften 35 (1991), 1–37.
D.J. Clements, and B.D.O. Anderson,Singular optimal control. The linear-quadratic problem. Lecture Notes in Control and Informations Science, Vol. 5, Springer-Verlag, Berlin, 1978.
R. Fletcher,Practical methods of optimization, Second edition, John Wiley & Sons, New York, NY 1987.
I.V. Girsanov,Lectures on mathematical theory of extremum problems, Lecture Notes in Economics and Mathematical Systems 67, Springer-Verlag, Berlin, 1972.
W.W. Hager, “Lipschitz continuity for constrained processes,”SIAM J. Control and Optimization 17 (1979), 321–337.
W.W. Hager, “Multiplier methods for nonlinear optimal control,”SIAM J. Numer. Anal. 17 (1990), 1061–1080.
K.C.P. Machielsen, “Numerical solution of optimal control problems with state constraints by sequential quadratic programming in function space,”CWI Tract 53, Amsterdam, 1987.
K. Malanowski, “Second order conditions and constraint qualifications in is stability and sensitivity analysis of solutions to optimization problems in Hilbert spaces,”Appl. Math. Optim. 25 (1992) 51–79.
K. Malanowski, “Two norm approach in stability and sensitivity analysis of optimization and optimal control problems,” (submitted 1991).
H. Maurer, “First-and second-order sufficient optimality conditions in mathematical programming and optimal control,”Math. Programming Study 14 (1981), 163–177.
H. Maurer, W. Pesch, “Solution differentiability for nonlinear parametric control problems,”Schwerpunktprogramm der Deutschen Forschungsgemeinschaft “Anwendungsbezogene Optimierung und Steuerung,” Report No. 316, 1991.
S.M. Robinson, “Perturbed Kuhn-Tucker points and rates of convergence for a class of nonlinear-programming algorithms,”Math. Programming 7 (1974), 1–16.
S.M. Robinson, “Regularity and stability for convex multivalued functions,”Math. of Oper. Res. 1 (1976), 130–143.
S.M. Robinson, “Strongly regular generalized equations,”Math. of Oper. Res. 5 (1980), 43–62.
S.M. Robinson, “Local structure of feasible sets in nonlinear programming, Part III: Stability and sensitivity,”Math. Programming Study 30 (1987), 45–66.
J. Stoer, “Principles of sequential quadratic programming methods for solving nonlinear programs,” in:Computational Mathematical Programming, Nato ASI Series, Vol. F15, K. Schittkowski (ed.), Springer-Verlag, Berlin, 1985, 165–207.
R.B. Wilson, “A simplical algorithm for concave programming,” Ph.D. Dissertation, Harvard Univ. Graduate School of Business Administration, Cambridge, MA, 1963.
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Alt, W., Malanowski, K. The Lagrange-Newton method for nonlinear optimal control problems. Comput Optim Applic 2, 77–100 (1993). https://doi.org/10.1007/BF01299143
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DOI: https://doi.org/10.1007/BF01299143