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Pointwise quasi-Newton method for unconstrained optimal control problems. II. (English) Zbl 0795.49023
Summary: The necessary optimality conditions for an unconstrained optimal control problem are used to derive a quasi-Newton method, where the update involves only second-order derivative terms. A pointwise update which was presented in part I of this paper [the first and second author, Numer. Math. 55, No. 2, 159-176 (1989; Zbl 0661.65068)] is changed to allow for more general second-order sufficiency conditions in the control problem. In particular, pointwise versions of the Broyden, PSB, and SR1 update are considered. A convergence rate theorem is given for the Broyden and PSB versions.

49M15Newton-type methods in calculus of variations
65K10Optimization techniques (numerical methods)
Full Text: DOI
[1] Kelley, C. T., andSachs, E. W.,A Pointwise Quasi-Newton Method for Unconstrained Optimal Control Problems, Numerische Mathematik, Vol. 55, pp. 159-176, 1989. · Zbl 0649.65039 · doi:10.1007/BF01406512
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[4] Lee, E. B., andMarkus, L.,Foundations of Optimal Control Theory, Wiley, New York, New York, 1967. · Zbl 0159.13201
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[6] Dennis, J. E., andSchnabel, R. B.,Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, Englewood Cliffs, New Jersey, 1983. · Zbl 0579.65058
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[8] Watson, B.,Quasi-Newton Methoden für Minimierungsprobleme mit Strukturierter Hesse-Matrix, Diploma Thesis, Universität Trier, Trier, Germany, 1990.
[9] Osborne, M. R., andSun, L. P.,A New Approach to the Symmetric Rank-One Updating Algorithm, Technical Report, Department of Statistics, IAS, Australian National University, 1988.
[10] Conn, A. R., Gould, N. I. M., andToint, P. L.,Convergence of Quasi-Newton Matrices Generated by the Symmetric Rank-One Update, Mathematical Programming, Vol. 50, pp. 177-195, 1991. · Zbl 0737.90062 · doi:10.1007/BF01594934