Quantized Distributed Optimization Schemes; a monotone operator approach

Jake Jonkman

Recently, the effects of quantization on the Primal-Dual Method of Multipliers were studied. In this thesis, we have used this method as an example to further investigate the effects of quantization on distributed optimization schemes in a much broader sense. Using monotone operator theory, the effect of quantization on all distributed optimization algorithms that can be cast as a monotone operator was researched for two different problem subclasses. The averaging problem was used as an example of a quadratic problem, while the Gaussian channel capacity problem was an example of the non-linear problem subclass. A fixed bit rate quantizer was used in combination with a dynamic cell width, to analyse the robustness of distributed optimization schemes against quantization effects. In particular, we have shown that for practical implementations it is possible to incorporate fixed bit rate quantization with dynamic cell width in a distributed optimization algorithm without loss of performance for both problem classes.

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