Distributed primal–dual interior-point methods for solving tree-structured coupled convex problems using message-passing. (4th May 2017)

• Record Type: Journal Article
• Authors: Khoshfetrat Pakazad, Sina; Hansson, Anders; Andersen, Martin S.; Nielsen, Isak
• Is Part Of: Optimization methods and software. Volume 32:Number 3(2017)
• Page Start: 401
• Page End: 435
• Publication Date: 2017-05-04
• Subjects: distributed optimization -- primal–dual interior-point method -- message-passing -- high precision solution; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2016.1213839
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : In this paper, we propose a distributed algorithm for solving coupled problems with chordal sparsity or an inherent tree structure which relies on primal–dual interior-point methods. We achieve this by distributing the computations at each iteration, using message-passing. In comparison to existing distributed algorithms for solving such problems, this algorithm requires far fewer iterations to converge to a solution with high accuracy. Furthermore, it is possible to compute an upper-bound for the number of required iterations which, unlike existing methods, only depends on the coupling structure in the problem. We illustrate the performance of our proposed method using a set of numerical examples.