A nonmonotone line search for the LBFGS method in parabolic optimal control problems

Omid Solaymani Fard; Farhad Sarani; Akbar Hashemi Borzabadi; Hadi Nosratipour

Kybernetika (2019)

  • Volume: 55, Issue: 1, page 183-202
  • ISSN: 0023-5954

Abstract

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In this paper a nonmonotone limited memory BFGS (NLBFGS) method is applied for approximately solving optimal control problems (OCPs) governed by one-dimensional parabolic partial differential equations. A discretized optimal control problem is obtained by using piecewise linear finite element and well-known backward Euler methods. Afterwards, regarding the implicit function theorem, the optimal control problem is transformed into an unconstrained nonlinear optimization problem (UNOP). Finally the obtained UNOP is solved by utilizing the NLBFGS method. In comparison to other existing methods, the NLBFGS method shows a significant improvement especially for nonlinear and ill-posed control problems.

How to cite

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Solaymani Fard, Omid, et al. "A nonmonotone line search for the LBFGS method in parabolic optimal control problems." Kybernetika 55.1 (2019): 183-202. <http://eudml.org/doc/294329>.

@article{SolaymaniFard2019,
abstract = {In this paper a nonmonotone limited memory BFGS (NLBFGS) method is applied for approximately solving optimal control problems (OCPs) governed by one-dimensional parabolic partial differential equations. A discretized optimal control problem is obtained by using piecewise linear finite element and well-known backward Euler methods. Afterwards, regarding the implicit function theorem, the optimal control problem is transformed into an unconstrained nonlinear optimization problem (UNOP). Finally the obtained UNOP is solved by utilizing the NLBFGS method. In comparison to other existing methods, the NLBFGS method shows a significant improvement especially for nonlinear and ill-posed control problems.},
author = {Solaymani Fard, Omid, Sarani, Farhad, Hashemi Borzabadi, Akbar, Nosratipour, Hadi},
journal = {Kybernetika},
keywords = {optimal control; parabolic partial differential equations; backward Euler method; nonmonotone LBFGS method},
language = {eng},
number = {1},
pages = {183-202},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A nonmonotone line search for the LBFGS method in parabolic optimal control problems},
url = {http://eudml.org/doc/294329},
volume = {55},
year = {2019},
}

TY - JOUR
AU - Solaymani Fard, Omid
AU - Sarani, Farhad
AU - Hashemi Borzabadi, Akbar
AU - Nosratipour, Hadi
TI - A nonmonotone line search for the LBFGS method in parabolic optimal control problems
JO - Kybernetika
PY - 2019
PB - Institute of Information Theory and Automation AS CR
VL - 55
IS - 1
SP - 183
EP - 202
AB - In this paper a nonmonotone limited memory BFGS (NLBFGS) method is applied for approximately solving optimal control problems (OCPs) governed by one-dimensional parabolic partial differential equations. A discretized optimal control problem is obtained by using piecewise linear finite element and well-known backward Euler methods. Afterwards, regarding the implicit function theorem, the optimal control problem is transformed into an unconstrained nonlinear optimization problem (UNOP). Finally the obtained UNOP is solved by utilizing the NLBFGS method. In comparison to other existing methods, the NLBFGS method shows a significant improvement especially for nonlinear and ill-posed control problems.
LA - eng
KW - optimal control; parabolic partial differential equations; backward Euler method; nonmonotone LBFGS method
UR - http://eudml.org/doc/294329
ER -

References

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