Primal-dual subgradient method

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In these notes, an extension of the subgradient method is presented in Section 8 (page 30). The method is described so quickly and neither convergence analysis (compared to classical subgradient for example) nor related references are discussed.

I would like to know more about these and googled but did not find anything.

I saw in the References a paper of Nesterov titled "Primal-dual subgradient methods for convex problems", however, this does not seem to be the same method.

Thank you for any suggestions.