A variable smoothing algorithm for solving convex optimization problems

Radu Boţ () and Christopher Hendrich ()

TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, 2015, vol. 23, issue 1, 124-150

Abstract: In this article, we propose a method for solving unconstrained optimization problems with convex and Lipschitz continuous objective functions. By making use of the Moreau envelopes of the functions occurring in the objective, we smooth them to convex and differentiable functions with Lipschitz continuous gradients using both variable and constant smoothing parameters. The resulting problem is solved via an accelerated first-order method and this allows us to recover approximately the optimal solutions to the initial optimization problem with a rate of convergence of order $$\mathcal {O}\left( \tfrac{\ln k}{k}\right) $$ O ln k k for variable smoothing and of order $$\mathcal {O}\left( \tfrac{1}{k}\right) $$ O 1 k for constant smoothing. Some numerical experiments employing the variable smoothing method in image processing and in supervised learning classification are also presented. Copyright Sociedad de Estadística e Investigación Operativa 2015

Keywords: Moreau envelope; Regularization; Variable smoothing; Fast gradient method; 90C25; 90C46; 47A52 (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://hdl.handle.net/10.1007/s11750-014-0326-z (text/html)
Access to full text is restricted to subscribers.

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:spr:topjnl:v:23:y:2015:i:1:p:124-150

Ordering information: This journal article can be ordered from
http://link.springer.de/orders.htm

DOI: 10.1007/s11750-014-0326-z

Access Statistics for this article

TOP: An Official Journal of the Spanish Society of Statistics and Operations Research is currently edited by Juan José Salazar González and Gustavo Bergantiños

More articles in TOP: An Official Journal of the Spanish Society of Statistics and Operations Research from Springer, Sociedad de Estadística e Investigación Operativa
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().