An approach to improve ill-conditioned steepest descent methods, application to a parabolic optimal control problem via time domain decomposition
Résumé
In this paper we present a new steepest-descent type algorithm for convex optimization problems. The method combines a Newton technique together with time domain decomposition in order to achieve the optimal step-length for the given set of descent directions. This is a parallel algorithm, where the parallel tasks turn on the control during a specific time-window and turn it off elsewhere. This new technique significantly improves computational time compared with recognized methods. Convergence analysis of the algorithm is provided for an arbitrary choice of partition. Numerical experiments are presented to illustrate the efficiency of our algorithm.
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