- 2015, SFoCM. Greedy algorithms which use only function evaluations are applied to convex optimization in a general Banach space (Formula presented.). Along with algorithms that use exact evaluations, algorithms with approximate evaluations are treated. A priori upper bounds for the convergence rate of the proposed algorithms are given. These bounds depend on the smoothness of the objective function and the sparsity or compressibility (with respect to a given dictionary) of a point in (Formula presented.) where the minimum is attained.