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A subgradient method based on gradient sampling for solving convex optimization problems

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Based on the gradient sampling technique, we present a subgradient algorithm to solve the nondifferentiable convex optimization problem with an extended real-valued objective function. A feature of our algorithm is the approximation of subgradient at a point via random sampling of (relative) gradients at nearby points, and then taking convex combinations of these (relative) gradients. We prove that our algorithm converges to an optimal solution with probability 1. Numerical results demonstrate that our algorithm performs favourably compared with existing subgradient algorithms on applications considered.
Original languageEnglish
Pages (from-to)1559-1584
Number of pages26
JournalNumerical Functional Analysis and Optimization
Issue number12
Early online date9 Dec 2015
Publication statusPublished - 31 Dec 2015


  • NFAOacceptedpaper

    Rights statement: This is an Accepted Manuscript of an article published by Taylor & Francis in Numerical Functional Analysis and Optimization Vol.36, Issue 12, available online:

    Accepted author manuscript (Post-print), 1.46 MB, PDF document

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