Active Set Complexity of the Away-Step Frank--Wolfe Algorithm
- Author(s)
- Immanuel Bomze, Francesco Rinaldi, Damiano Zeffiro
- Abstract
In this paper, we study active set identification results for the away-step Frank Wolfe algorithm in different settings. We first prove a local identification property that we apply, in combination with a convergence hypothesis, to get an active set identification result. We then prove, for nonconvex objectives, a novel O(1/root k) convergence rate result and active set identification for different step sizes (under suitable assumptions on the set of stationary points). By exploiting those results, we also give explicit active set complexity bounds for both strongly convex and nonconvex objectives. While we initially consider the probability simplex as feasible set, in an appendix we show how to adapt some of our results to generic polytopes.
- Organisation(s)
- Department of Statistics and Operations Research, Research Network Data Science, Research Platform Governance of digital practices
- External organisation(s)
- University of Padova
- Journal
- SIAM Journal on Optimization
- Volume
- 30
- Pages
- 2470-2500
- No. of pages
- 31
- ISSN
- 1052-6234
- DOI
- https://doi.org/doi.org/10.1137/19M1309419
- Publication date
- 09-2020
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 101015 Operations research
- Keywords
- ASJC Scopus subject areas
- Software, Theoretical Computer Science
- Portal url
- https://ucris.univie.ac.at/portal/en/publications/active-set-complexity-of-the-awaystep-frankwolfe-algorithm(abbf5277-ea87-4c9f-9db6-0a0ac9afb0e3).html