In this paper we propose some Newton-type algorithms for the numerical solution of both unconstrained and constrained discrete-time optimal control problems. The approach followed here is based on a suitable augmented Lagrangian function whose unconstrained minimization yields the solution of the optimal control problem and the associated multipliers. We show that the Hessian matrix of the augmented Lagrangian function has a sparse structure which allows the use of an efficient decomposition scheme for the computation of the Newton's direction. In addition, consistent approximations of the Newton's direction are described. These approximations may allow a further reduction of the computational cost. Two numerical examples are reported.

A Newton-type Computing Technique for Optimal Control Problems / DI PILLO, Gianni; Grippo, Luigi; F., Lampariello. - In: OPTIMAL CONTROL APPLICATIONS & METHODS. - ISSN 0143-2087. - STAMPA. - 5:2(1984), pp. 149-166. [10.1002/oca.4660050207]

A Newton-type Computing Technique for Optimal Control Problems

DI PILLO, Gianni;GRIPPO, Luigi;
1984

Abstract

In this paper we propose some Newton-type algorithms for the numerical solution of both unconstrained and constrained discrete-time optimal control problems. The approach followed here is based on a suitable augmented Lagrangian function whose unconstrained minimization yields the solution of the optimal control problem and the associated multipliers. We show that the Hessian matrix of the augmented Lagrangian function has a sparse structure which allows the use of an efficient decomposition scheme for the computation of the Newton's direction. In addition, consistent approximations of the Newton's direction are described. These approximations may allow a further reduction of the computational cost. Two numerical examples are reported.
1984
discrete-time optimal control; newton-type algorithms
01 Pubblicazione su rivista::01a Articolo in rivista
A Newton-type Computing Technique for Optimal Control Problems / DI PILLO, Gianni; Grippo, Luigi; F., Lampariello. - In: OPTIMAL CONTROL APPLICATIONS & METHODS. - ISSN 0143-2087. - STAMPA. - 5:2(1984), pp. 149-166. [10.1002/oca.4660050207]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/242909
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