Double smoothing technique for infinite-dimensional optimization problems with applications to optimal control

Olivier Devolder (), François Glineur and Yurii Nesterov ()
Additional contact information
Olivier Devolder: Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium
Yurii Nesterov: Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium

No 2010034, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

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. As a result, our method has complexity O (1/[epsilon] ln 1/[epsilon]) gradient iterations, where [epsilon] is the desired accuracy of the solution of the primal-dual problem. 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 (search for similar items in EconPapers)
Date: 2010-07-01
New Economics Papers: this item is included in nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://sites.uclouvain.be/core/publications/coredp/coredp2010.html (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:cor:louvco:2010034

Access Statistics for this paper

More papers in LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) Voie du Roman Pays 34, 1348 Louvain-la-Neuve (Belgium). Contact information at EDIRC.
Bibliographic data for series maintained by Alain GILLIS ().