I've searched Google, but it seems that only research journal papers appear in search results, where some new, improved, or specialized extragradient method is discussed. I've also searched Wikipedia and Wolfram MathWorld.


I would like to perhaps know the straightforward definition of that, instead of deducing it from a number of articles, where the basic/original method is not defined.



What is an extragradient method?
This is the key reference: G.M. Korpelevich, "The extragradient method for finding saddle points and other problems." *Ekonomika i Matematicheskie Metody* **12** (1976): 747-756.


I have not found this article online, but you can find a brief description [here](http://www.fixedpointtheoryandapplications.com/content/pdf/1687-1812-2013-185.pdf) (page 1 and 2) and a more extensive description (with a convergence proof) [here](http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3073511/pdf/nihms-232812.pdf) (pages 1-6). Volume II of [Facchinei and Pang](http://books.google.nl/books?id=lX_7Rce3_Q0C) also has a chapter on the method.


