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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. Auslender,Optimisation—Méthodes numériques (Masson, Paris, 1976).
M. Frank and P. Wolfe, “An algorithm for quadratic programming“,Naval Research Logistics Quarterly 3 (1956) 95–110.
D.G. Luenberger,Introduction to linear and nonlinear programming (Addison-Wesley, Reading, MA, 1973).
R.T. Rockafellar,Convex analysis (Princeton University Press, Princeton, NJ, 1970).
P. Wolfe, “Convergence theory in nonlinear programming“, in: J. Abadie, ed.,Integer and nonlinear programming (North-Holland, Amsterdam, 1970).
W.I. Zangwill,Nonlinear programming: A unified approach (Prentice-Hall, Englewood Cliffs, NJ, 1969).
Author information
Authors and Affiliations
Additional information
Research supported by FCAC (Québec) and NSERC (Canada).
Rights and permissions
About this article
Cite this article
GuéLat, J., Marcotte, P. Some comments on Wolfe's ‘away step’. Mathematical Programming 35, 110–119 (1986). https://doi.org/10.1007/BF01589445
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01589445