CCCP is Frank-Wolfe in disguise

Part of Advances in Neural Information Processing Systems 35 (NeurIPS 2022) Main Conference Track

Bibtex Paper Supplemental


Alp Yurtsever, Suvrit Sra


This paper uncovers a simple but rather surprising connection: it shows that the well-known convex-concave procedure (CCCP) and its generalization to constrained problems are both special cases of the Frank-Wolfe (FW) method. This connection not only provides insight of deep (in our opinion) pedagogical value, but also transfers the recently discovered convergence theory of nonconvex Frank-Wolfe methods immediately to CCCP, closing a long-standing gap in its non-asymptotic convergence theory. We hope the viewpoint uncovered by this paper spurs the transfer of other advances made for FW to both CCCP and its generalizations.