Active Set Complexity of the Away-step Frank-Wolfe Algorithm

In this paper, we study active set identification results for the away-step Frank-Wolfe algorithm in different settings. We first prove a local identification property that we apply, in combination with a convergence hypothesis, to get an active set identification result. We then prove, in the nonconvex case, a novel O(1/ √k) convergence rate result and … Read more

”Active-set complexity” of proximal gradient: How long does it take to find the sparsity pattern?

Proximal gradient methods have been found to be highly effective for solving minimization problems with non-negative constraints or L1-regularization. Under suitable nondegeneracy conditions, it is known that these algorithms identify the optimal sparsity pattern for these types of problems in a finite number of iterations. However, it is not known how many iterations this may … Read more