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

In this paper, relations between distributed consensus-based optimization and a network resource allocation problem are considered. It is shown that first-order gradient algorithm for distributed consensus-based optimization can be used for finding an optimal solution of distributed resource allocation with synchronous protocol under weaker assumptions than those given in the literature. Moreover, second-order gradient algorithm for distributed consensus-based optimization is presented that can be employed for solving distributed resource allocation problems. As a result, several algorithms used for distributed consensus-based optimization can now be applied to derive distributed algorithms for resource allocation. It is shown that first and second order gradient algorithms for distributed resource allocation can be utilized for finding an optimal solution of distributed consensus-based optimization as well. The results presented in this paper can be applied to time-varying or random directed networks with or without synchronous protocols with arbitrary initialization. Finally, a numerical example of a distributed estimation in wireless sensor networks is given to demonstrate the results.