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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Andrea Cristofari & Marianna De Santis & Stefano Lucidi & Francesco Rinaldi, 2016. "New Active-Set Frank-Wolfe Variants for Minimization over the Simplex and the L1-Ball," DIAG Technical Reports 2016-06, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    • Handle: RePEc:aeg:report:2016-06
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    File URL: http://www.dis.uniroma1.it/~bibdis/RePEc/aeg/report/2016-06.pdf
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    Keywords

    Active-set methods ; Frank-Wolfe ; Unit simplex ; L1-ball.;
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