Open this publication in new window or tab >>2025 (English)In: NeuriPS 2025: Downloads, 2025Conference paper, Poster (with or without abstract) (Refereed)
Abstract [en]
We introduce a new projection-free (Frank-Wolfe) method for optimizing structured nonconvex functions that are expressed as a difference of two convex functions. This problem class subsumes smooth nonconvex minimization, positioning our method as a promising alternative to the classical Frank-Wolfe algorithm. DC decompositions are not unique; by carefully selecting a decomposition, we can better exploit the problem structure, improve computational efficiency, and adapt to the underlying problem geometry to find better local solutions. We prove that the proposed method achieves a first-order stationary point in iterations, matching the complexity of the standard Frank-Wolfe algorithm for smooth non-convex minimization in general. Specific decompositions can, for instance, yield a gradient-efficient variant that requires only calls to the gradient oracle by reusing computed gradients over multiple iterations. Finally, we present numerical experiments demonstrating the effectiveness of the proposed method compared to other projection-free algorithms.
National Category
Computational Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:umu:diva-248742 (URN)
Conference
NeuriPS 2025, The Thirty-Ninth Annual Conference on Neural Information Processing Systems, San Diego, USA, December 1, 2025
2026-01-202026-01-202026-01-22Bibliographically approved