Signal Processing Seminar

Distributed Convex Optimization: A Monotone Perspective

Thomas Sherson

Over the last few decades, methods of parallel and distributed computation have become essential tools in a wide range of applications such as machine learning, wireless sensor network processing and big data signal processing. Motivated by this point and the synergy between signal processing and convex optimization, in this work we demonstrate recent results in the area of distributed optimisation to facilitate such computation. In particular we highlight the primal dual method of multipliers (PDMM), a relatively recent algorithm proposed for distributed optimization. We demonstrate how PDMM can be derived from classic monotone operator theory which in turn provides insight into previously unknown convergence results for the algorithm. Using this insight we generalise PDMM to solve the class of separable problems with separable constraints and analyze how, in the case of strongly convex and smooth functions, the convergence rate of PDMM is influenced by the underlying network topology.

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