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I need an English translation of the paper "A method for unconstrained convex minimization problem with the rate of convergence $O\left(\frac{1}{k^2}\right)$" by Yurii Nesterov, 1983. I have been able to find the Russian version but I don't know Russian. In some papers (where this paper is cited), it is written that an english translation is available in the Soviet Math Doklady. I have not been able to find one. If anyone has the English version of the paper, please share it or tell me how to get it.

Link to the original russian paper.

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    $\begingroup$ The paper is very short, and contains little text. What exactly do you need from it that Google Translate/DeepL + mathematical knowledge cannot provide you? $\endgroup$
    – Carl-Fredrik Nyberg Brodda
    Jun 15, 2021 at 12:13
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    $\begingroup$ For example, just copying in the first paragraph into GT becomes: "The article proposes a method for solving the convex programming problem in the Hilbert space E. Unlike most of the convex programming methods proposed earlier, this method constructs a minimizing sequence of points [symbols] which is not relaxation. This the feature allows you to minimize the computational costs at each step." This is a good translation, and I bet DeepL will do better! (edit: and, just as I wrote that, Sean Eberhard confirms this!). $\endgroup$
    – Carl-Fredrik Nyberg Brodda
    Jun 15, 2021 at 12:15

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Somebody here recently suggested DeepL on a similar question, and it does work remarkably well. You can just copy and paste into their website (even the Cyrillic). I just tried it on Section 1 of your paper and this is what it spat out:

  1. This paper presents a method for solving a convex programming problem in Hilbert space E. Unlike the majority of convex programming methods proposed earlier, this method constructs a minimizing sequence of points {xk \k=Qi which is not relaxational. This feature allows to minimize computational cost at each step. At the same time, it is possible to obtain for this method an unimprovable estimate of the convergence speed on the class of problems under consideration (see [ 1 ]) .

Translated with www.DeepL.com/Translator (free version)

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This journal has been translated:

Nesterov, Yu. E. A method of solving a convex programming problem with convergence rate 0(1/k2). (English. Russian original) Zbl 0535.90071 Sov. Math., Dokl. 27, 372-376 (1983); translation from Dokl. Akad. Nauk SSSR 269, 543-547 (1983).

Most university libraries used to subscribe this. If your library does not have it, you can use ILL.

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  • $\begingroup$ Actually, I know it has been translated into a journal Soviet Mathematics Dokaldy by AMS but the issue is I am not able to find such a journal on its website. Can you guide me a bit? Also, what is ILL? $\endgroup$
    – A Q
    Jun 15, 2021 at 12:49
  • $\begingroup$ @AQ: the journal is defunct after the fall of the USSR (since there is no longer a Soviet academy of sciences). So you will not find it listed as a current publication. AMS never digitized that journal, so you won't find back issues online. Most libraries have access to the original paper publications. Many (if you ask the librarian nicely) will scan the relevant article for you. $\endgroup$
    – Willie Wong
    Jun 15, 2021 at 14:31
  • $\begingroup$ ILL = InterLibrary Loan $\endgroup$
    – Willie Wong
    Jun 15, 2021 at 14:32
  • $\begingroup$ @WillieWong Thank you very much for the info. $\endgroup$
    – A Q
    Jun 17, 2021 at 18:07
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I think this is a translated version of it.

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