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Zbl 0795.49023
Kelley, C.T.; Sachs, E.W.; Watson, B.
Pointwise quasi-Newton method for unconstrained optimal control problems. II. (English)
[J] J. Optimization Theory Appl. 71, No.3, 535-547 (1991). ISSN 0022-3239; ISSN 1573-2878/e

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.

MSC 2000:: *49M15 Methods of Newton-Raphson, Galerkin and Ritz types
65K10 Optimization techniques (numerical methods)

Keywords: necessary optimality conditions; unconstrained optimal control; quasi- Newton method; second-order sufficiency conditions

Citations: Zbl 0649.65039; Zbl 0661.65068

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