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IMA Journal of Numerical Analysis Advance Access originally published online on April 2, 2008
IMA Journal of Numerical Analysis 2009 29(2):315-331; doi:10.1093/imanum/drn016
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© The author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

The spectral gradient method for unconstrained optimal control problems

J. I. Ardenghi{dagger}, T. I. Gibelli{ddagger} and M. C. Maciel§

Departmento de Matemática, Universidad Nacional del Sur, Av. Alem 1253, 8000 Bahía Blanca, Argentina

{dagger} Email: ardenghi{at}criba.edu.ar

{ddagger} Email: tgibelli{at}uns.edu.ar

§ Email: immaciel{at}criba.edu.ar

Received on 16 December 2004. Revised on 23 December 2007.


  Abstract

Optimal control problems and their discretized form can be viewed as optimization problems. Kelley and Sachs have already solved the discretized problem by using quasi-Newton methods. In this contribution, the problem is solved by a low-cost algorithm, the spectral gradient method, which is suitable for large-scale problems. The convergence behaviour of the method to finite-dimensional approximation is analysed. Numerical examples are given and the reported results show the good performance of the algorithm when it is applied to large optimal control problems.

Key Words: optimal control; nonmonotone line search; spectral gradient method


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