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This paper aims at proposing a procedure to derive distributed algorithms fordistributed consensus-based optimization by using distributed algorithms fornetwork resource allocation and vice versa over switching networks with/withoutsynchronous protocol. It is shown that first-order gradient distributedconsensus-based optimization algorithms can be used for finding an optimalsolution of distributed resource allocation with synchronous protocol underweaker assumptions than those given in the literature for non-switching(static) networks. It is shown that first-order gradient distributed resourceallocation algorithms can be utilized for finding an optimal solution ofdistributed consensus-based optimization. The results presented here can beapplied to time-varying and random directed networks with or withoutsynchronous protocol with arbitrary initialization. As a result, severalalgorithms can now be used to derive distributed algorithms for bothconsensus-based optimization and resource allocation, that can overcomelimitations of the existing results. While the focus of this paper is on thefirst-order gradient algorithms, it is to be noted that the results also workwith second-order gradient algorithms.

Reciprocity of Algorithms Solving Distributed Consensus-Based Optimization and Distributed Resource Allocation