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Double smoothing technique for infinite-dimensional optimization problems with applications to Optimal Control.

Olivier Devolder (Olivier.devolder***at***uclouvain.be)
François Glineur (Francois.Glineur***at***uclouvain.be)
Yurii Nesterov (Yurii.Nesterov***at***uclouvain.be)

Abstract: In this paper, we propose an efficient technique for solving some infinite-dimensional problems over the sets of functions of time. In our problem, besides the convex point-wise constraints on state variables, we have convex coupling constraints with finite-dimensional image. Hence, we can formulate a finite-dimensional dual problem, which can be solved by efficient gradient methods. We show that it is possible to reconstruct an approximate primal solution. In order to accelerate our schemes, we apply double-smoothing technique. Our approach covers, in particular, the optimal control problems with trajectory governed by a system of ordinary differential equations. The additional requirement could be that the trajectory crosses in certain moments of time some convex sets.

Keywords: Convex optimization, optimal control, fast gradient methods, complexity bounds, smoothing technique

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Infinite Dimensional Optimization

Citation: [ note that an updated version of this paper is available at http://www.optimization-online.org/DB_HTML/2011/01/2896.html ] CORE Discussion paper 2010/34, Center for Operations Research and Econometrics (CORE), Universite catholique de Louvain (UCL), Belgium

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Entry Submitted: 08/03/2010
Entry Accepted: 08/03/2010
Entry Last Modified: 05/26/2011

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