Electron. J. Diff. Equ., Vol. 2011 (2011), No. 44, pp. 1-16.

Optimizing second-order differential equation systems

Tamas Hajba

Abstract:
In this article we study some continuous versions of the Fletcher-Reeves iteration for minimization described by a system of second-order differential equations. This problem has been studied in earlier papers [19, 20] under the assumption that the minimizing function is strongly convex. Now instead of the strong convexity, only the convexity of the minimizing function will be required. We will use the Tikhonov regularization [28, 29] to obtain the minimal norm solution as the asymptotically stable limit point of the trajectories.

Submitted October 25, 2010. Published March 31, 2011.
Math Subject Classifications: 90C25, 65K05, 34D05.
Key Words: Fletcher-Reeves iteration; second-order differential equation; minimizing trajectory; stationary point in limit; Lyapunov-type methods.

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Tamás Hajba
Department of Mathematics and Computer Science
Faculty of Engineering Sciences, Széchenyi István
University, Egyetem tér 1., H-9026 Gyor, Hungary
email: hajbat@sze.hu, Tel +36 (96) 503-400, Fax +36 (96) 613-657

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