Infeasibility Detection in the Alternating Direction Method of Multipliers for Convex Optimization

Goran Banjac, Paul Goulart, Bartolomeo Stellato, Stephen Boyd

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

3 Scopus citations

Abstract

The alternating direction method of multipliers (ADMM) is a powerful operator splitting technique for solving structured optimization problems. For convex optimization problems, it is well-known that the iterates generated by ADMM converge to a solution provided that it exists. If a solution does not exist then the ADMM iterates do not converge. Nevertheless, we show that the ADMM iterates yield conclusive information regarding problem infeasibility for a wide class of convex optimization problems including both quadratic and conic programs. In particular, we show that in the limit the ADMM iterates either satisfy a set of first-order optimality conditions or produce a certificate of either primal or dual infeasibility. Based on these results, we propose termination criteria for detecting primal and dual infeasibility in ADMM.

Original languageEnglish (US)
Title of host publication2018 UKACC 12th International Conference on Control, CONTROL 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages340
Number of pages1
ISBN (Electronic)9781538628645
DOIs
StatePublished - Oct 31 2018
Externally publishedYes
EventUKACC 12th International Conference on Control, CONTROL 2018 - Sheffield, United Kingdom
Duration: Sep 5 2018Sep 7 2018

Publication series

Name2018 UKACC 12th International Conference on Control, CONTROL 2018

Conference

ConferenceUKACC 12th International Conference on Control, CONTROL 2018
CountryUnited Kingdom
CitySheffield
Period9/5/189/7/18

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Control and Optimization

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