Solving infinite-dimensional optimization problems by polynomial approximation

Olivier Devolder (), François Glineur and Yurii Nesterov ()
Additional contact information
Olivier Devolder: Center for Operations Research and Econometrics (CORE), Université catholique de Louvain (UCL), Louvain la Neuve, Belgium
Yurii Nesterov: Center for Operations Research and Econometrics (CORE), Université catholique de Louvain (UCL), Louvain la Neuve, Belgium

No 2010029, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: In this paper, we solve a class of convex infinite-dimensional optimization problems using a numerical approximation method that does not rely on discretization. Instead, we restrict the decision variable to a sequence of finite-dimensional linear subspaces of the original infinite-dimensional space and solve the corresponding finite-dimensional problems in a efficient way using structured convex optimization techniques. We prove that, under some reasonable assumptions, the sequence of these optimal values converges to the optimal value of the original infinite-dimensional problem and give an explicit description of the corresponding rate of convergence.

Keywords: infinite-dimensional optimization; polynomial approximation; semidefinite programming; positive polynomials; optimization in normed spaces; continuous linear programs; infinite programming (search for similar items in EconPapers)
Date: 2010-06-01
New Economics Papers: this item is included in nep-cmp
References: Add references at CitEc
Citations: View citations in EconPapers (3)

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

Related works:
Working Paper: Solving infinite-dimensional optimizaiton problems by polynomial approximation (2010)
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:2010029

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 ().