Alternating conditional gradient method for convex feasibility problems

The classical convex feasibility problem in a finite dimensional Euclidean space consists of finding point the intersection two sets. In present paper we are interested particular instances this problem. First, assume to know how compute an exact projection onto one sets involved and other set is compact such that conditional gradient (CondG) method can be used for computing efficiently inexact on it. Second, both CondG projections them. We combine alternating with design new method, which seen as feasible version alternate method. proposed generates different sequences belonging each set, converge them whenever it not empty. If empty, then points respective whose distance between equal consideration. Numerical experiments provided illustrate practical behavior