New Active-Set Frank-Wolfe Variants for Minimization over the Simplex and the L1-Ball

Andrea Cristofari (), Marianna De Santis (), Stefano Lucidi () and Francesco Rinaldi ()
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Andrea Cristofari: Department of Computer, Control and Management Engineering Antonio Ruberti (DIAG), University of Rome La Sapienza, Rome, Italy
Marianna De Santis: Department of Mathematics, University of Padova
Stefano Lucidi: Department of Computer, Control and Management Engineering Antonio Ruberti (DIAG), University of Rome La Sapienza, Rome, Italy
Francesco Rinaldi: Department of Mathematics, University of Padova

No 2016-06, DIAG Technical Reports from Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza"

Abstract: In this paper, we are concerned with minimization problems over the unit simplex. Here, we propose the use of an active-set estimate that enables us to define an algorithmic framework where the variables estimated active and those estimated non-active are updated separately at each iteration. In particular, we consider different variants of the Frank-Wolfe direction to be combined with the proposed active-set strategy, proving the convergence of the algorithm for each of them. Then, we focus on the problem of minimizing a function over the L1-ball, showing how our algorithmic framework can be efficiently adapted to this problem.Preliminary numerical results show the benefits of the proposed active-set estimate.

Keywords: Active-set methods; Frank-Wolfe; Unit simplex; L1-ball. (search for similar items in EconPapers)
Date: 2016
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