Chebushev Greedy Algorithm in convex optimization
This work addresses the need for efficient sparse approximation methods in convex optimization, particularly for applications in signal processing or machine learning, but it appears incremental as it extends an existing algorithm to a more general setting.
The paper tackles the problem of constructing sparse approximate solutions for convex optimization problems in Banach spaces by applying the Chebyshev Greedy Algorithm, a generalization of Orthogonal Matching Pursuit, and proves rate of convergence results in the style of Lebesgue-type inequalities.
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. Rate of convergence results in a style of the Lebesgue-type inequalities are proved.