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Dual Convergence Estimates for a Family of Greedy Algorithms in Banach Spaces

  • S. P. SidorovEmail author
  • S. V. Mironov
  • M. G. Pleshakov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10710)

Abstract

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.

Keywords

Greedy algorithms Nonlinear optimization Sparsity 

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • S. P. Sidorov
    • 1
    Email author
  • S. V. Mironov
    • 1
  • M. G. Pleshakov
    • 1
  1. 1.Saratov State UniversitySaratovRussian Federation

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