A REGULARIZATION OF THE FRANK-WOLFE METHOD AND UNIFICATION OF CERTAINNONLINEAR-PROGRAMMING METHODS

The Frank-Wolfe linearization technique is a popular feasible directio n algorithm for the solution of certain linearly constrained nonlinear problems. The popularity of this technique is due in part to its abil ity to exploit special constraint structures, such as network structur es, and in part to the fact that it decomposes nonseparable problems o ver Cartesian product sets. However, the linearization which induces t hese advantages is also the source of the main disadvantages of the me thod: a sublinear rate of convergence and zigzagging behaviour. In ord er to avoid these disadvantages, a regularization penalty term is adde d to the objective of the direction generating subproblem. This result s in a generic feasible direction method which also includes certain k nown nonlinear programming methods.