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New Active-Set Frank-Wolfe Variants for Minimization over the Simplex and the l1-Ball

Cristofari Andrea(cristofari***at***dis.uniroma1.it)
De Santis Marianna(desantis***at***math.unipd.it)
Lucidi Stefano(lucidi***at***dis.uniroma1.it)
Rinaldi Francesco(rinaldi***at***math.unipd.it)

Abstract: In this paper, we describe a new active-set algorithmic framework for minimizing a function over the simplex. The method is quite general and encompasses different active-set Frank-Wolfe variants. In particular, we analyze convergence (when using Armijo line search in the calculation of the stepsize) for the active-set versions of standard Frank-Wolfe, away-step Frank-Wolfe and pairwise Frank-Wolfe. Then, we focus on convex optimization problems, and prove that all active- set variants converge at a linear rate under weaker assumptions than the classical counterparts. We further explain how to adapt our framework in order to handle the problem of minimizing a function over the l1-ball. Finally, we report numerical experiments showing the efficiency of the various active-set Frank-Wolfe variants.

Keywords: Active-set methods, Frank-Wolfe algorithm, Unit simplex, l1-Ball

Category 1: Nonlinear Optimization


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Entry Submitted: 03/22/2017
Entry Accepted: 03/22/2017
Entry Last Modified: 03/22/2017

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