Journal
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Volume 63, Issue 12, Pages 4331-4337Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2018.2816104
Keywords
Constrained optimization; distributed algorithms; epigraph form; random-fixed projected algorithm; time-varying unbalanced digraphs
Funding
- National Natural Science Foundation of China [61722308, 41576101]
- Tsinghua University Initiative Scientific Research Program
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This paper considers a distributed convex optimization problem with inequality constraints over time-varying unbalanced digraphs, where the cost function is a sum of local objective functions, and each node of the graph only knows its local objective and inequality constraints. Although there is a vast body of literature on distributed optimization. most of them require the graph to be balanced, which is quite restrictive and not necessary. To solve it, this work proposes a novel idea of using the epigraph form of the constrained optimization. which can be easily used to study time-varying unbalanced digraphs. Under local communications, a simple iterative algorithm is then designed for each node. We prove that if the graph is uniformly jointly strongly connected, each node asymptotically converges to some common optimal solution.
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