Greedy algorithms in convex optimization on Banach spaces

Chebyshev Greedy Algorithm is a generalization of the well known Orthogonal Matching Pursuit defined in a Hilbert space to the case of Banach spaces. We apply this algorithm for constructing sparse approximate solutions (with respect to a given dictionary) to convex optimization problems. Along with algorithms that use exact evaluations, algorithms with approximate evaluations are discussed. Convergence and rate of convergence results are obtained.