CCCP is Frank-Wolfe in disguise

Alp Yurtsever, Suvrit Sra

Keywords: convex-concave procedure, cccp, frank-wolfe, conditional gradient method, difference of convex programming, expectation maximization, sinkhorn

TL;DR: This paper shows that the well-known convex-concave procedure (CCCP) and its generalization to constrained problems are both special cases of the Frank-Wolfe method.

Abstract: 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.