用自适应方法提升非凸优化效率，适合大规模约束问题。
Scalable DC Optimization via Adaptive Frank-Wolfe Algorithms
- 结合改进的Frank-Wolfe算法与热启动策略
- 在约束条件下实现高效求解，计算开销显著降低
- 适用于大规模可扩展的差分凸优化场景
本文研究在紧致凸可行集 $P$ 上最小化光滑凸函数之差的问题，即 $\min_{x \in P} f(x) - g(x)$，其中 $f$ 光滑，$g$ 满足Lipschitz连续。该实证研究基于Maskan等[2025]的框架，引入先进的Frank-Wolfe变体以减少计算开销。我们通过实验表明，将混合成对条件梯度（BPCG）算法[2022]与热启动相结合，并利用Maskan等[2025]提出的自适应误差界，可高效求解约束型差分凸（DC）优化问题。所得算法为投影无关的高效率、可扩展优化方法。
原文摘要 · Abstract (English)
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.
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