The paper examines four weak relaxed greedy algorithms for finding approximate sparse solutions of convex optimization problems in a Banach space. First, we present a review of primal results on the convergence rate of the algorithms based on the geometric properties of the objective function. Then, using the ideas of [16], we define the duality gap and prove that the duality gap is a certificate for the current approximation to the optimal solution. Finally, we find estimates of the dependence of the duality gap values on the number of iterations for weak greedy algorithms.
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