Distributed convex optimization as a tool for solving ƒ-consensus problems

For a group of networked agents, ƒ-consensus means reaching consensus upon the value of a desired function, ƒ, of the initial state of the individual agents. This paper shows how one can often convert a given ƒ-consensus problem into a suitable distributed convex optimization (DCO) problem, which can be readily solved with existing DCO algorithms in the literature. A computational advantage may then accrue. Particular classes of ƒ-consensus problems shown to be solvable with this approach include weighted power mean consensus, and kth smallest value or kth order statistic consensus (which includes max/min consensus and median consensus as special cases).