Distributed Algorithm for Achieving Minimum l1 Norm Solutions of Linear Equation
Jingqiu Zhou, Xuan Wang, Shaoshuai Mou, Brian D. O. Anderson · 2018
Ahstract- This paper proposes a distributed algorithm for multi-agent networks to achieve a minimum$l_{1}$-norm solution to a linear equation$Ax=b$where$A$has full row rank. When the underlying network is undirected and fixed, it is proved that the proposed algorithm drive all agents' individual states to converge in finite-time to the same minimum$l_{1}$-norm solution. Numerical simulations are also provided as validation of the proposed algorithms.