Random minibatch projection algorithms for convex feasibility problems

Angelia Nedic, Ion Necoara

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

Abstract

This paper deals with the convex feasibility problem where the feasible set is given as the intersection of a (possibly infinite) number of closed convex sets. We assume that each set is specified algebraically as a convex inequality, where the associated convex function may be even non-differentiable. We present and analyze a random minibatch projection algorithm using special subgradient iterations for solving the convex feasibility problem described by the functional constraints. The updates are performed based on parallel random observations of several constraint components. For this minibatch method we derive asymptotic convergence results and, under some linear regularity condition for the functional constraints, we prove linear convergence rate. We also derive conditions under which the rate depends explicitly on the minibatch size. To the best of our knowledge, this work is the first proving that random minibatch subgradient based projection updates have a better complexity than their single-sample variants.

Original languageEnglish (US)
Title of host publication2019 IEEE 58th Conference on Decision and Control, CDC 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1507-1512
Number of pages6
ISBN (Electronic)9781728113982
DOIs
StatePublished - Dec 2019
Event58th IEEE Conference on Decision and Control, CDC 2019 - Nice, France
Duration: Dec 11 2019Dec 13 2019

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2019-December
ISSN (Print)0743-1546

Conference

Conference58th IEEE Conference on Decision and Control, CDC 2019
CountryFrance
CityNice
Period12/11/1912/13/19

Keywords

  • Convex sets
  • convergence analysis
  • feasibility problem
  • functional constraints
  • random minibatch projections

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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