Geodesic
Optimizing second-order differential equation systems
Electronic Journal of Differential Equations, Tome 2011 (2011).

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Summary: 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.
Classification : 90C25, 65K05, 34D05
Keywords: fletcher-reeves iteration, second-order differential equation, minimizing trajectory, stationary point in limit, Lyapunov-type methods 
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     author = {Hajba, Tam\'as},
     title = {Optimizing second-order differential equation systems},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2011},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a83/}
}
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Hajba, Tamás. Optimizing second-order differential equation systems. Electronic Journal of Differential Equations, Tome 2011 (2011). http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a83/