  We study the averaging-based distributed optimization solvers over random
networks. We show a general result on the convergence of such schemes using
weight-matrices that are row-stochastic almost surely and column-stochastic in
expectation for a broad class of dependent weight-matrix sequences. In addition
to implying many of the previously known results on this domain, our work shows
the robustness of distributed optimization results to link-failure. Also, it
provides a new tool for synthesizing distributed optimization algorithms. {To
prove our main theorem, we establish new results on the rate of convergence
analysis of averaging dynamics over (dependent) random networks. These
secondary results, along with the required martingale-type results to establish
them, might be of interest to broader research endeavors in distributed
computation over random networks.
