Distributed Solutions for Loosely Coupled Feasibility Problems Using Proximal Splitting Methods

Sina Khoshfetrat Pakazad, Martin Skovgaard Andersen, Anders Hansson

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

In this paper,we consider convex feasibility problems (CFPs) where the underlying sets are loosely coupled, and we propose several algorithms to solve such problems in a distributed manner. These algorithms are obtained by applying proximal splitting methods to convex minimization reformulations of CFPs. We also put forth distributed convergence tests which enable us to establish feasibility or infeasibility of the problem distributedly, and we provide convergence rate results. Under the assumption that the problem is feasible and boundedly linearly regular, these convergence results are given in terms of the distance of the iterates to the feasible set, which are similar to those of classical projection methods. In case the feasibility problem is infeasible, we provide convergence rate results that concern the convergence of certain error bounds.
Original languageEnglish
JournalOptimization Methods and Software
Number of pages34
ISSN1055-6788
DOIs
Publication statusPublished - 2014

Keywords

  • feasible / infeasible convex feasibility problems
  • proximal splitting
  • distributed solution
  • flow feasibility problem

Cite this