  This paper is concerned with the Frank--Wolfe algorithm for a special class
of {\it non-compact} constrained optimization problems. The notion of
asymptotic cone is used to introduce this class of problems as well as to
establish that the algorithm is well defined. These problems, with closed and
convex constraint set, are characterized by two conditions on the gradient of
the objective function. The first establishes that the gradient of the
objective function is Lipschitz continuous, which is quite usual in the
analysis of this algorithm. The second, which is new in this subject,
establishes that the gradient belongs to the interior of the dual asymptotic
cone of the constraint set. Classical results on the asymptotic behavior and
iteration-complexity bounds for the sequence generated by the Frank--Wolfe
algorithm are extended to this new class of problems. Examples of problems with
non-compact constraints and objective functions satisfying the aforementioned
conditions are also provided.
