Projection-free accelerated method for convex optimization

In this paper, we propose a projection-free accelerated method for solving convex optimization problems with unbounded feasible set. The method is an accelerated gradient scheme such that each projection subproblem is approximately solved by means of a conditional gradient scheme. Under reasonable a...

Full description

Saved in:

Bibliographic Details
Published in:	Optimization methods & software 2022-01, Vol.37 (1), p.214-240
Main Authors:	Gonçalves, Max L. N., Melo, Jefferson G., Monteiro, Renato D. C.
Format:	Article
Language:	eng
Subjects:	accelerated method conditional gradient method Convexity first-order methods Iterative methods Optimization Projection-free method
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	In this paper, we propose a projection-free accelerated method for solving convex optimization problems with unbounded feasible set. The method is an accelerated gradient scheme such that each projection subproblem is approximately solved by means of a conditional gradient scheme. Under reasonable assumptions, it is shown that an ϵ-approximate solution (concept related to the optimal value of the problem) is obtained in at most gradient evaluations and linear oracle calls. We also discuss a notion of approximate solution based on the first-order optimality condition of the problem and present iteration-complexity results for the proposed method to obtain an approximate solution in this sense. Finally, numerical experiments illustrating the practical behaviour of the proposed scheme are discussed.
ISSN:	1055-6788 1029-4937