Gradient methods with regularization for constrained optimization problems and their complexity estimates

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.

Keywords:

• Convex optimization
• Hilbert space
• gradient projection method
• conditional gradient method
• strong convergence
• complexity estimates

Notes

No potential conflict of interest was reported by the author.

Additional information

Funding

The results of this work were obtained within the state assignment of the Ministry of Science and Education of Russia [project number 1.460.2016/1.4]. In this work, the author was also supported by Russian Foundation for Basic Research [project number 13-01-00368-a].