Year: 2025
Type: article
Abstract: . We propose a novel generalization of the conditional gradient (CG/Frank–Wolfe) algorithm for minimizing a smooth function [Formula: see text] under an intersection of compact convex sets, using a first-order oracle for [Formula: see text] and linear minimization oracles (LMOs) for the individual sets. Although this computational framework presents many advantages, there are only a small number of algorithms which require one LMO evaluation per set per iteration; furthermore, these algorithms require [Formula: see text] to be convex. Our algorithm appears to be the first in this class which is proven to also converge in the nonconvex setting. Our approach combines a penalty method and a product-space relaxation. We show that one CG step is a sufficient subroutine for our penalty method to converge, and we provide several analytical results on the product-space relaxation’s properties and connections to other problems in optimization. We prove that our average Frank–Wolfe gap converges at a rate of [Formula: see text]—only a log factor worse than the vanilla CG algorithm with one set.
Source: SIAM Journal on Optimization
DOI: 10.1137/24m1638008
Authors: Zev Woodstock, Sebastian Pokutta
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: G1372115314, G2033548659, Forschungscampus MODAL - Mathematical Optimization and Data Analysis Laboratories - zweite Förderphase (Stabilisierung), EXC 2046: MATH+: Berlin Mathematics Research Center, G7802408855, Forschungscampus Modal - Mathematical Optimization and Data Analysis Laboratories. Antrag auf die erste Hauptphase (Implementierung) des Forschungscampus Modal
OpenAlex ID: W4407426247