Randomized Algorithms for Distributed Nonlinear Optimization Under Sparsity Constraints

8 years 9 days ago

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Abstract—Distributed optimization in multi-agent systems under sparsity constraints has recently received a lot of attention. In this paper, we consider the in-network minimization of a continuously differentiable nonlinear function which is a combination of local agent objective functions subject to sparsity constraints on the variables. A crucial issue of in-network optimization is the handling of the communications, which may be expensive. This calls for efﬁcient algorithms, that are able to reduce the number of required communication links and transmitted messages. To this end, we focus on asynchronous and randomized distributed techniques. Based on consensus techniques and iterative hard thresholding methods, we propose three methods that attempt to minimize the given function, promoting sparsity of the solution: asynchronous hard thresholding (AHT), broadcast hard thresholding (BHT), and gossip hard thresholding (GHT). Although similar in many aspects, it is difﬁcult to obt...

Chiara Ravazzi, Sophie M. Fosson, Enrico Magli

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