@inproceedings{353283453375456a9f9aa937140b015d,

title = "On the analysis of reflected gradient and splitting methods for monotone stochastic variational inequality problems",

abstract = "Stochastic generalizations of the extragradient method are complicated by a key challenge: the scheme requires two projections on a convex set and two evaluations of the map for every major iteration. We consider two related avenues where every iteration requires a single projection: (i) A projected reflected gradient (PRG) method requiring a single evaluation of the map and a single projection; and (ii) A modified backward-forward splitting (MBFS) method that requires two evaluations of the map and a single projection. We make the following contributions: (a) We prove almost sure convergence of the iterates to a random point in the solution set for the stochastic PRG scheme under a weak sharpness requirement; (b) We prove that the mean of the gap function associated with the averaged sequence diminishes to zero at the optimal rate of O(1/√N) for both schemes where N is the iteration index.",

author = "Shisheng Cui and Shanbhag, {Uday V.}",

year = "2016",

month = dec,

day = "27",

doi = "10.1109/CDC.2016.7798955",

language = "English (US)",

series = "2016 IEEE 55th Conference on Decision and Control, CDC 2016",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "4510--4515",

booktitle = "2016 IEEE 55th Conference on Decision and Control, CDC 2016",

address = "United States",

note = "55th IEEE Conference on Decision and Control, CDC 2016 ; Conference date: 12-12-2016 Through 14-12-2016",

}