Scalable DC Optimization via Adaptive Frank-Wolfe Algorithms

TL;DR

This paper introduces an efficient, scalable, projection-free algorithm for constrained difference-of-convex (DC) optimization, combining advanced Frank-Wolfe variants with adaptive error bounds to reduce computational costs.

Contribution

It integrates Blended Pairwise Conditional Gradients with adaptive error bounds to improve efficiency in solving constrained DC problems.

Findings

Efficiently solves constrained DC problems using the combined algorithm.

Demonstrates scalability and reduced computational overhead.

Validates approach through empirical experiments.

Abstract

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.