Distributed Optimisation under a Weight-unbalanced Digraph

Distributed optimisation (DO) problems in application to networked multi-agent system (MAS) have been an intriguing topic for research among different research communities. Despite the substantial number of works in this field over the past decade, the existing literature lacks a generalised algorithm for solving the DO problem for a strongly-connected weight unbalanced graph. This paper presents an information state dynamics for optimising the convex global objective function in a distributed manner under a strongly-connected weight-unbalanced digraph. Unlike few of the existing algorithms, the proposed dynamics does not require any global information, rather it solely depends on the locally available information and the information that the agent receives from the neighbours only. Numerical simulations with a comparative study with the state-of-the-art algorithm solving a DO problem under a weight-unbalanced digraph are also demonstrated in the paper to prove the claims.