This is a great way to remember DRS. However, there is a technical detail missing: The matrix $M$ is not positive definite. Indeed, for all $x \in X$, we have . Thus, convergence of DRS cannot be deduced from the paper by Rockafellar.

If and , then the metric

can be used in place of $M$. This results in the primal-dual algorithm of Chambolle and Pock (http://www.optimization-online.org/DB_FILE/2010/06/2646.pdf), and weak convergence follows by the results of Rockafellar. Thus, DRS is really a limiting case of a class of primal-dual algorithms. I believe the first paper to notice this connection is by He and Yuan: http://www.math.hkbu.edu.hk/~xmyuan/Paper/HeYuan-SIIMS-2nd.pdf.

Since the paper by He and Yuan, several other metrics have been developed. A few are summarized by Pesquet and Repetti in http://arxiv.org/pdf/1406.6404.pdf, and by myself in http://arxiv.org/pdf/1408.4419v1.pdf

Damek

]]>https://es.wikipedia.org/wiki/Regla_de_Villalobos

I could be in English. I could use a virtual translator, but are not very accurate.

Greetings.

]]>https://es.wikipedia.org/wiki/Regla_de_Villalobos

I could be in English. I could use a virtual translator, but are not very accurate.

Greetings

]]>http://math.stackexchange.com/questions/110438/is-there-an-explicit-isomorphism-between-l-infty0-1-and-ell-infty/110983#110983 ]]>

If plugins are not available, you can still try to edit your theme and add the second code block from this page http://docs.mathjax.org/en/latest/configuration.html to your header.php (in the ). ]]>

Nevertheless, this does not solve your figure/TikZ problem, it makes formulae look nicer.

Kind regards from Kaiserslautern,

Ronny

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