# Scalable DC Optimization via Adaptive Frank-Wolfe Algorithms

arXiv: https://arxiv.org/abs/2507.17545 · HTML: https://mlsanity.com/paper/2507.17545/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 66 references that are in the map.
- First posted on arXiv 23 Jul 2025.

## Builds on (most cited first, 30 of 42)

- [On the Global Linear Convergence of Frank-Wolfe Optimization Variants](https://mlsanity.com/paper/1511.05932/) (2015)
- [Convergence Rate of Frank-Wolfe for Non-Convex Objectives](https://mlsanity.com/paper/1607.00345/) (2016)
- [Faster Rates for the Frank-Wolfe Method over Strongly-Convex Sets](https://mlsanity.com/paper/1406.1305/) (2014)
- [A gradient sampling method with complexity guarantees for Lipschitz functions in high and low dimensions](https://mlsanity.com/paper/2112.06969/) (2021)
- [Disciplined Convex-Concave Programming](https://mlsanity.com/paper/1604.02639/) (2016)
- [Complexity of Linear Minimization and Projection on Some Sets](https://mlsanity.com/paper/2101.10040/) (2021)
- [Conditional Gradient Methods](https://mlsanity.com/paper/2211.14103/) (2022)
- [An Extended Frank-Wolfe Method with "In-Face" Directions, and its Application to Low-Rank Matrix Completion](https://mlsanity.com/paper/1511.02204/) (2015)
- [Convergence guarantees for a class of non-convex and non-smooth optimization problems](https://mlsanity.com/paper/1804.09629/) (2018)
- [Fixed-point algorithms for learning determinantal point processes](https://mlsanity.com/paper/1508.00792/) (2015)
- [Linearly Convergent Frank-Wolfe with Backtracking Line-Search](https://mlsanity.com/paper/1806.05123/) (2018)
- [Non-convex Conditional Gradient Sliding](https://mlsanity.com/paper/1708.04783/) (2017)
- [Boosting Frank-Wolfe by Chasing Gradients](https://mlsanity.com/paper/2003.06369/) (2020)
- [Linear-memory and Decomposition-invariant Linearly Convergent Conditional Gradient Algorithm for Structured Polytopes](https://mlsanity.com/paper/1605.06492/) (2016)
- [On the rate of convergence of the Difference-of-Convex Algorithm (DCA)](https://mlsanity.com/paper/2109.13566/) (2021)
- [The cost of nonconvexity in deterministic nonsmooth optimization](https://mlsanity.com/paper/2210.00652/) (2022)
- [The Frank-Wolfe algorithm: a short introduction](https://mlsanity.com/paper/2311.05313/) (2023)
- [Accelerating the DC algorithm for smooth functions](https://mlsanity.com/paper/1507.07375/) (2015)
- [Lazifying Conditional Gradient Algorithms](https://mlsanity.com/paper/1610.05120/) (2016)
- [Locally Accelerated Conditional Gradients](https://mlsanity.com/paper/1906.07867/) (2019)
- [FrankWolfe.jl: a high-performance and flexible toolbox for Frank-Wolfe algorithms and Conditional Gradients](https://mlsanity.com/paper/2104.06675/) (2021)
- [CCCP is Frank-Wolfe in disguise](https://mlsanity.com/paper/2206.12014/) (2022)
- [Restarting Frank-Wolfe: Faster Rates Under H"olderian Error Bounds](https://mlsanity.com/paper/1810.02429/) (2018)
- [Best-Effort Adaptation](https://mlsanity.com/paper/2305.05816/) (2023)
- [The Boosted DC Algorithm for linearly constrained DC programming](https://mlsanity.com/paper/1908.01138/) (2019)
- [Parameter-free Locally Accelerated Conditional Gradients](https://mlsanity.com/paper/2102.06806/) (2021)
- [A boosted DC algorithm for non-differentiable DC components with non-monotone line search](https://mlsanity.com/paper/2111.01290/) (2021)
- [Conditional Accelerated Lazy Stochastic Gradient Descent](https://mlsanity.com/paper/1703.05840/) (2017)
- [Local and Global Uniform Convexity Conditions](https://mlsanity.com/paper/2102.05134/) (2021)
- [Minding the Gaps for Block Frank-Wolfe Optimization of Structured SVMs](https://mlsanity.com/paper/1605.09346/) (2016)

## Built on by (most cited first, 1 of 1)

- [Analytical Evaluation of DCA Convergence Properties for Minimizing Prediction Functions of Gaussian RBF Support Vector Regression](https://mlsanity.com/paper/2606.03559/) (2026)

## Abstract (arXiv)

We consider the problem of minimizing a difference of (smooth) convex functions over a compact convex feasible region P, i.e., minx ∈ 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.