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A Discrete-time Distributed Algorithm for Minimum l1-Norm Solution of an Under-determined Linear Equation Set⁎This work was supported by fundings from Northrop Grumman Corporation (NGC-REALM and NGCRC), Data61-CSIRO, and the Australian Research Council's Discovery Projects DP-160104500 and DP190100887. Corresponding Author: Shaoshuai Mou. Issue 2 (2020)
Record Type:
Journal Article
Title:
A Discrete-time Distributed Algorithm for Minimum l1-Norm Solution of an Under-determined Linear Equation Set⁎This work was supported by fundings from Northrop Grumman Corporation (NGC-REALM and NGCRC), Data61-CSIRO, and the Australian Research Council's Discovery Projects DP-160104500 and DP190100887. Corresponding Author: Shaoshuai Mou. Issue 2 (2020)
Main Title:
A Discrete-time Distributed Algorithm for Minimum l1-Norm Solution of an Under-determined Linear Equation Set⁎This work was supported by fundings from Northrop Grumman Corporation (NGC-REALM and NGCRC), Data61-CSIRO, and the Australian Research Council's Discovery Projects DP-160104500 and DP190100887. Corresponding Author: Shaoshuai Mou.
Abstract: This paper proposes a discrete-time, distributed algorithm for multi-agent networks to achieve the minimum l 1 -norm solution to a group of linear equations known to possess a family of solutions. We assume each agent in the network knows only one equation and can communicate with only its neighbors. The algorithm is developed based on a combination of the projection-consensus idea and the sub-gradient descent method. Given the underlying network graph to be directed and strongly connected, we prove that the algorithm enables all agents to achieve a common minimum l 1 -norm solution. The major difficulty to be dealt with is the non-smooth nature of the norm and the lack of strict convexity of the associated relevant performance index.