Print Email Facebook Twitter Derivation and Analysis of the Primal-Dual Method of Multipliers Based on Monotone Operator Theory Title Derivation and Analysis of the Primal-Dual Method of Multipliers Based on Monotone Operator Theory Author Sherson, T.W. (TU Delft Signal Processing Systems) Heusdens, R. (TU Delft Signal Processing Systems) Kleijn, W.B. (TU Delft Signal Processing Systems; Victoria University of Wellington) Date 2019 Abstract In this paper, we present a novel derivation of an existing algorithm for distributed optimization termed the primal-dual method of multipliers (PDMM). In contrast to its initial derivation, monotone operator theory is used to connect PDMM with other first-order methods such as Douglas-Rachford splitting and the alternating direction method of multipliers, thus, providing insight into its operation. In particular, we show how PDMM combines a lifted dual form in conjunction with Peaceman-Rachford splitting to facilitate distributed optimization in undirected networks. We additionally demonstrate sufficient conditions for primal convergence for strongly convex differentiable functions and strengthen this result for strongly convex functions with Lipschitz continuous gradients by introducing a primal geometric convergence bound. Subject distributed optimizationmonotone operatorPrimal-Dual method of multipliers (PDMM) To reference this document use: http://resolver.tudelft.nl/uuid:822093d3-5614-41ee-844c-a86a19e2db22 DOI https://doi.org/10.1109/TSIPN.2018.2876754 ISSN 2373-776X Source IEEE Transactions on Signal and Information Processing over Networks, 5 (2), 334-347 Bibliographical note Accepted author manuscript Part of collection Institutional Repository Document type journal article Rights © 2019 T.W. Sherson, R. Heusdens, W.B. Kleijn Files PDF main.pdf 849.79 KB Close viewer /islandora/object/uuid:822093d3-5614-41ee-844c-a86a19e2db22/datastream/OBJ/view