Abstract

. In the context of optimal control of ordinary differential equations, we prove local superlinear convergence and constraint identification results for an extension of the projected Newton method of Bertsekas. The estimates are also valid for discretized versions of the method-problem pair. Key words. projected Newton iteration, optimal control AMS(MOS) subject classifications. 47H17, 49K15, 49M15, 65J15, 65K10 1. Introduction. In many areas of optimal control the problems are formulated with simple constraints on the control. For this type of problems, the gradient projection type algorithms have proven to be quite successful, because they are able to take into account the structure of the underlying optimization problem. Another interesting feature of these methods is that they often can be formulated in infinite dimensional spaces which is important for the application to optimal control problems. In general, let H denote a Hilbert space and for some closed convex subset U 2 H c...

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