Mathematical Programming

, Volume 35, Issue 1, pp 110–119 | Cite as

Some comments on Wolfe's ‘away step’

  • Jacques GuéLat
  • Patrice Marcotte
Article

Abstract

We give a detailed proof, under slightly weaker conditions on the objective function, that a modified Frank-Wolfe algorithm based on Wolfe's ‘away step’ strategy can achieve geometric convergence, provided a strict complementarity assumption holds.

Key words

Convex programming Frank-Wolfe algorithm 

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References

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    A. Auslender,Optimisation—Méthodes numériques (Masson, Paris, 1976).Google Scholar
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    M. Frank and P. Wolfe, “An algorithm for quadratic programming“,Naval Research Logistics Quarterly 3 (1956) 95–110.Google Scholar
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    D.G. Luenberger,Introduction to linear and nonlinear programming (Addison-Wesley, Reading, MA, 1973).Google Scholar
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    R.T. Rockafellar,Convex analysis (Princeton University Press, Princeton, NJ, 1970).Google Scholar
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    P. Wolfe, “Convergence theory in nonlinear programming“, in: J. Abadie, ed.,Integer and nonlinear programming (North-Holland, Amsterdam, 1970).Google Scholar
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    W.I. Zangwill,Nonlinear programming: A unified approach (Prentice-Hall, Englewood Cliffs, NJ, 1969).Google Scholar

Copyright information

© The Mathematical Programming Society, Inc. 1986

Authors and Affiliations

  • Jacques GuéLat
    • 1
  • Patrice Marcotte
    • 2
  1. 1.Centre de recherche sur les transportsUniversité de MontréalMontréalCanada
  2. 2.Collège Militaire Royal de Saint-Jean and Centre de recherche sur les transportsUniversité de MontréalMontréalCanada

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