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A newton‐type computing technique for optimal control problems
Author(s) -
Pillo G. Di,
Grippo L.,
Lampariello F.
Publication year - 1984
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.4660050207
Subject(s) - hessian matrix , augmented lagrangian method , newton's method , optimal control , computation , minification , mathematical optimization , quasi newton method , mathematics , function (biology) , reduction (mathematics) , type (biology) , lagrangian , computer science , algorithm , nonlinear system , ecology , physics , geometry , quantum mechanics , evolutionary biology , biology
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.