On the analysis of reflected gradient and splitting methods for monotone stochastic variational inequality problems

Shisheng Cui, Uday V. Shanbhag

Research output: Chapter in Book/Report/Conference proceedingConference contribution

9 Scopus citations

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.

Original languageEnglish (US)
Title of host publication2016 IEEE 55th Conference on Decision and Control, CDC 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4510-4515
Number of pages6
ISBN (Electronic)9781509018376
DOIs
StatePublished - Dec 27 2016
Event55th IEEE Conference on Decision and Control, CDC 2016 - Las Vegas, United States
Duration: Dec 12 2016Dec 14 2016

Publication series

Name2016 IEEE 55th Conference on Decision and Control, CDC 2016

Other

Other55th IEEE Conference on Decision and Control, CDC 2016
Country/TerritoryUnited States
CityLas Vegas
Period12/12/1612/14/16

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Decision Sciences (miscellaneous)
  • Control and Optimization

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