2013/06/28 by Sina Khoshfetrat Pakazad, Martin S. Andersen, Pakazad, Sina Khoshfetrat +3
Business, Management and Accounting · Computer Science · Mathematics · #90C25 #90C35 #90C90 #93A14 #93A15 #Advanced Optimization Algorithms Research #FOS: Mathematics #Facility Location and Emergency Management #G.1.10 #G.1.6 #G.2.2 #I.1.2 #Optimization and Control (math.OC) #Optimization and Variational Analysis #acm:90C25 #acm:90C35 #acm:90C90 #acm:93A14 #acm:93A15 #math.OC #msc:90C25 #msc:90C35 #msc:90C90 #msc:93A14 #msc:93A15
paper · pdf · doi:10.48550/arxiv.1306.6807
30 pages and 4 figures. Submitted to Optimization Methods and Softwares Journal
arxiv created 2013/06/28 · openalex publication_date 2013/06/28 · arxiv updated 2013/07/01 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
In this paper, we consider convex feasibility problems 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 convex feasibility problems. 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.