2025/04/30 by Aktas, Fatih Selim, Kroer, Christian
#FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2505.00221
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-Łojasiewicz (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 ℓ1 minimization algorithm for compressed sensing, and design a new algorithm for the semidefinite relaxation of the Max-Cut problem.