Distributed Random-Fixed Projected Algorithm for Constrained Optimization Over Digraphs*. Issue 1 (July 2017)

• Record Type: Journal Article
• Authors: Xie, Pei; You, Keyou; Song, Shiji; Wu, Cheng
• Is Part Of: IFAC-PapersOnLine. Volume 50:Issue 1(2017)
• Page Start: 14436
• Page End: 14441
• Publication Date: 2017-07
• Subjects: Distributed algorithms -- constrained optimization -- unbalanced digraphs -- epigraph form -- random-fixed projected algorithm; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2017.08.2284
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: This paper is concerned with a constrained optimization problem over a directed graph (digraph) of nodes, in which the cost function is a sum of local objectives, and each node only knows its local objective and constraints. To collaboratively solve the optimization, most of the existing works require the interaction graph to be balanced or "doubly-stochastic", which is quite restrictive and not necessary as shown in this paper. We focus on an epigraph form of the original optimization to resolve the "unbalanced" problem, and design a novel two-step recursive algorithm with a simple structure. Under strongly connected digraphs, we prove that each node asymptotically converges to some common optimal solution. Finally, simulations are performed to illustrate the effectiveness of the proposed algorithms.