Gradient methods with regularization for constrained optimization problems and their complexity estimates. (4th May 2018)

• Record Type: Journal Article
• Authors: Konnov, I. V.
• Is Part Of: Optimization. Volume 67:Number 5(2018)
• Page Start: 665
• Page End: 682
• Publication Date: 2018-05-04
• Subjects: Convex optimization -- Hilbert space -- gradient projection method -- conditional gradient method -- strong convergence -- complexity estimates; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2017.1416612
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: We suggest simple implementable modifications of conditional gradient and gradient projection methods for smooth convex optimization problems in Hilbert spaces. Usually, the custom methods attain only weak convergence. We prove strong convergence of the new versions and establish their complexity estimates, which appear similar to the convergence rate of the weakly convergent versions. Preliminary results of computational tests confirm efficiency of the proposed modification.