Convergence of the Lagrange-Newton method for optimal control problems

Kazimierz Malanowski

International Journal of Applied Mathematics and Computer Science (2004)

  • Volume: 14, Issue: 4, page 531-540
  • ISSN: 1641-876X

Abstract

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Convergence results for two Lagrange-Newton-type methods of solving optimal control problems are presented. It is shown how the methods can be applied to a class of optimal control problems for nonlinear ODEs, subject to mixed control-state constraints. The first method reduces to an SQP algorithm. It does not require any information on the structure of the optimal solution. The other one is the shooting method, where information on the structure of the optimal solution is exploited. In each case, conditions for well-posedness and local quadratic convergence are given. The scope of applicability is briefly discussed.

How to cite

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Malanowski, Kazimierz. "Convergence of the Lagrange-Newton method for optimal control problems." International Journal of Applied Mathematics and Computer Science 14.4 (2004): 531-540. <http://eudml.org/doc/207717>.

@article{Malanowski2004,
abstract = {Convergence results for two Lagrange-Newton-type methods of solving optimal control problems are presented. It is shown how the methods can be applied to a class of optimal control problems for nonlinear ODEs, subject to mixed control-state constraints. The first method reduces to an SQP algorithm. It does not require any information on the structure of the optimal solution. The other one is the shooting method, where information on the structure of the optimal solution is exploited. In each case, conditions for well-posedness and local quadratic convergence are given. The scope of applicability is briefly discussed.},
author = {Malanowski, Kazimierz},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {nonlinear ODEs; Lagrange-Newton method; mixed constraints; optimal control},
language = {eng},
number = {4},
pages = {531-540},
title = {Convergence of the Lagrange-Newton method for optimal control problems},
url = {http://eudml.org/doc/207717},
volume = {14},
year = {2004},
}

TY - JOUR
AU - Malanowski, Kazimierz
TI - Convergence of the Lagrange-Newton method for optimal control problems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2004
VL - 14
IS - 4
SP - 531
EP - 540
AB - Convergence results for two Lagrange-Newton-type methods of solving optimal control problems are presented. It is shown how the methods can be applied to a class of optimal control problems for nonlinear ODEs, subject to mixed control-state constraints. The first method reduces to an SQP algorithm. It does not require any information on the structure of the optimal solution. The other one is the shooting method, where information on the structure of the optimal solution is exploited. In each case, conditions for well-posedness and local quadratic convergence are given. The scope of applicability is briefly discussed.
LA - eng
KW - nonlinear ODEs; Lagrange-Newton method; mixed constraints; optimal control
UR - http://eudml.org/doc/207717
ER -

References

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