Strongly Convex Maximization via the Frank-Wolfe Algorithm with the Kurdyka-{\L}ojasiewicz Inequality
Abstract
We study the convergence properties of the 'greedy' Frank-Wolfe algorithm with a unit step size, for a convex maximization problem over a compact set. We assume the function satisfies smoothness and strong convexity. These assumptions together with the Kurdyka-{\L}ojasiewicz (KL) property, allow us to derive global asymptotic convergence for the sequence generated by the algorithm. Furthermore, we also derive a convergence rate that depends on the geometric properties of the problem. To illustrate the implications of the convergence result obtained, we prove a new convergence result for a sparse principal component analysis algorithm, propose a convergent reweighted minimization algorithm for compressed sensing, and design a new algorithm for the semidefinite relaxation of the Max-Cut problem.
Keywords
Cite
@article{arxiv.2505.00221,
title = {Strongly Convex Maximization via the Frank-Wolfe Algorithm with the Kurdyka-{\L}ojasiewicz Inequality},
author = {Fatih Selim Aktas and Christian Kroer},
journal= {arXiv preprint arXiv:2505.00221},
year = {2025}
}