A regularization of the Frank-Wolfe method and unification of certain nonlinear programming methods

The Frank-Wolfe linearization technique is a popular feasible direction algorithm for the solution of certain linearly constrained nonlinear problems. The popularity of this technique is due in part to its ability to exploit special constraint structures, such as network structures, and in part to t...

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Bibliographic Details
Published in:Mathematical programming 1994-02, Vol.65 (3), p.331-345
Main Author: MIGDALAS, A
Format: Article
Language:English
Subjects:
Applied sciences
Exact sciences and technology
Industrial Logistics
Industriell logistik
Mathematical programming
Operational research and scientific management
Operational research. Management science
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Summary:The Frank-Wolfe linearization technique is a popular feasible direction algorithm for the solution of certain linearly constrained nonlinear problems. The popularity of this technique is due in part to its ability to exploit special constraint structures, such as network structures, and in part to the fact that it decomposes nonseparable problems over Cartesian product sets. However, the linearization which induces these advantages is also the source of the main disadvantages of the method: a sublinear rate of convergence and zigzagging behaviour. In order to avoid these disadvantages, a regularization penalty term is added to the objective of the direction generating subproblem. This results in a generic feasible direction method which also includes certain known nonlinear programming methods
ISSN:0025-5610
1436-4646
1436-4646
DOI:10.1007/BF01581701