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While competing methods such as [[gradient descent]] for constrained optimization require a [[Projection (mathematics)|projection step]] back to the feasible set in each iteration, the Frank–Wolfe algorithm only needs the solution of a linear problem over the same set in each iteration, and automatically stays in the feasible set.
The convergence of the Frank–Wolfe algorithm is sublinear in general: the error in the objective function to the optimum is <math>O(1/k)</math> after ''k'' iterations, so long as the gradient is [[Lipschitz continuity|Lipschitz continuous]] with respect to some norm. The same convergence rate can also be shown if the sub-problems are only solved approximately.<ref>{{Cite journal | last1 = Dunn | first1 = J. C. | last2 = Harshbarger | first2 = S. | doi = 10.1016/0022-247X(78)90137-3 | title = Conditional gradient algorithms with open loop step size rules | journal = Journal of Mathematical Analysis and Applications | volume = 62 | issue = 2 | pages = 432 | year = 1978 | pmid = | pmc = | doi-access = free }}</ref>
The iterates of the algorithm can always be represented as a sparse convex combination of the extreme points of the feasible set, which has helped to the popularity of the algorithm for sparse greedy optimization in [[machine learning]] and [[signal processing]] problems,<ref>{{Cite journal | last1 = Clarkson | first1 = K. L. | title = Coresets, sparse greedy approximation, and the Frank-Wolfe algorithm | doi = 10.1145/1824777.1824783 | journal = ACM Transactions on Algorithms | volume = 6 | issue = 4 | pages = 1–30 | year = 2010 | pmid = | pmc = | citeseerx = 10.1.1.145.9299 }}</ref> as well as for example the optimization of [[flow network|minimum–cost flow]]s in [[Transport network|transportation network]]s.<ref>{{Cite journal | last1 = Fukushima | first1 = M. | title = A modified Frank-Wolfe algorithm for solving the traffic assignment problem | doi = 10.1016/0191-2615(84)90029-8 | journal = Transportation Research Part B: Methodological | volume = 18 | issue = 2 | pages = 169–177| year = 1984 | pmid = | pmc = }}</ref>
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