# A NEW APPROACH TO IMPROVE ILL-CONDITIONED PARABOLIC OPTIMAL CONTROL PROBLEM VIA TIME DOMAIN DECOMPOSITION

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Abstract : In this paper we present a new steepest-descent type algorithm for convex optimization problems. Our algorithm pieces the unknown into sub-blocs of unknowns and considers a partial optimization over each sub-bloc. In quadratic optimization, our method involves Newton technique to compute the step-lengths for the sub-blocs resulting descent directions. Our optimization method is fully parallel and easily implementable, we first presents it in a general linear algebra setting, then we highlight its applicability to a parabolic optimal control problem, where we consider the blocs of unknowns with respect to the time dependency of the control variable. The parallel tasks, in the last problem, turnon" the control during a specific time-window and turn it off" elsewhere. We show that our algorithm significantly improves the computational time compared with recognized methods. Convergence analysis of the new optimal control algorithm is provided for an arbitrary choice of partition. Numerical experiments are presented to illustrate the efficiency and the rapid convergence of the method.
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Cited literature [80 references]

https://hal.inria.fr/hal-00974285
Contributor : Mohamed Kamel Riahi Connect in order to contact the contributor
Submitted on : Wednesday, November 4, 2020 - 3:34:10 PM
Last modification on : Thursday, November 5, 2020 - 3:06:58 AM

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• HAL Id : hal-00974285, version 3

### Citation

Mohamed-Kamel Riahi. A NEW APPROACH TO IMPROVE ILL-CONDITIONED PARABOLIC OPTIMAL CONTROL PROBLEM VIA TIME DOMAIN DECOMPOSITION. 2020. ⟨hal-00974285v3⟩

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