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

Title:

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

Creator:

Fard, Omid Solaymani , Sarani, Farhad, Borzabadi , Akbar Hashemi, and Nosratipour, Hadi

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:fd103d61-0144-432c-9f13-0dc4dcac7115
uuid:fd103d61-0144-432c-9f13-0dc4dcac7115
doi:10.14736/kyb-2019-1-0183

Subject:

optimal control, parabolic partial differential equations, backward Euler method, and nonmonotone LBFGS method

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

183-202

Source:

Kybernetika | 2019 Volume:55 | Number:1

Harvested from:

CDK

Metadata only:

false