Simplified versions of the conditional gradient method

ABSTRACT

We suggest simple modifications of the conditional gradient method for smooth optimization problems, which maintain the basic convergence properties, but reduce the implementation cost of each iteration essentially. Namely, we propose an adaptive step-size procedure without any line-search and inexact solution of the direction finding subproblem. Preliminary results of computational tests confirm efficiency of the proposed modifications.

KEYWORDS:

• Optimization problems
• pseudo-convex function
• conditional gradient method
• simple adaptive step-size
• inexact direction finding subproblem
• convergence properties

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 90C25
• 90C30

Disclosure statement

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 No. 1.460.2016/1.4. In this work, the author was also supported by Russian Foundation for Basic Research, project No. 16-01-00408-a, and by the subsidy allocated to Kazan Federal University for the state assignment in the sphere of scientific activities, project No. 1.12878.2018/12.1.