When you have only box constraints I don't think Frank Wofle is very efficient. Frank Wolfe can handle more complex constraints. You should try a quasi newton algorithm like l-bfgs-b or a truncated newton conjugate gradient algorithm with projection.
From the looks of it (simple feasible set, convex objective, gradient available), Frank-Wolfe indeed makes a lot of sense here.
I can point out that there exist many variants of the algorithm, and that several are implemented in this recent Julia package. This can give you a quick way to experiments various algorithmic configurations.
If you do decide to ...