Scalable DC Optimization via Adaptive Frank-Wolfe Algorithms
This work addresses constrained DC optimization problems, which are incremental improvements for computational optimization in machine learning and related fields.
The paper tackles the problem of minimizing a difference of convex functions over a compact convex region by integrating advanced Frank-Wolfe variants to reduce computational overhead, resulting in a highly efficient and scalable projection-free algorithm for constrained DC optimization.
We consider the problem of minimizing a difference of (smooth) convex functions over a compact convex feasible region $P$, i.e., $\min_{x \in P} f(x) - g(x)$, with smooth $f$ and Lipschitz continuous $g$. This computational study builds upon and complements the framework of Maskan et al. [2025] by integrating advanced Frank-Wolfe variants to reduce computational overhead. We empirically show that constrained DC problems can be efficiently solved using a combination of the Blended Pairwise Conditional Gradients (BPCG) algorithm [Tsuji et al., 2022] with warm-starting and the adaptive error bound from Maskan et al. [2025]. The result is a highly efficient and scalable projection-free algorithm for constrained DC optimization.