Distributed Algorithm for Achieving Minimum l1 Norm Solutions of Linear Equation

نویسندگان

  • Jingqiu Zhou
  • Wang Xuan
  • Shaoshuai Mou
چکیده

This paper proposes a distributed algorithm for multi-agent networks to achieve a minimum l1-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 l1-norm solution. Numerical simulations are also provided as validation of the proposed algorithms.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

An L1-norm method for generating all of efficient solutions of multi-objective integer linear programming problem

This paper extends the proposed method by Jahanshahloo et al. (2004) (a method for generating all the efficient solutions of a 0–1 multi-objective linear programming problem, Asia-Pacific Journal of Operational Research). This paper considers the recession direction for a multi-objective integer linear programming (MOILP) problem and presents necessary and sufficient conditions to have unbounde...

متن کامل

Finite-Time Distributed Linear Equation Solver for Minimum $l_1$ Norm Solutions

This paper proposes distributed algorithms for multi-agent networks to achieve a solution in finite time to a linear equation Ax = b where A has full row rank, and with the minimum l1-norm in the underdetermined case (where A has more columns than rows). The underlying network is assumed to be undirected and fixed, and an analytical proof is provided for the proposed algorithm to drive all agen...

متن کامل

‎A matrix LSQR algorithm for solving constrained linear operator equations

In this work‎, ‎an iterative method based on a matrix form of LSQR algorithm is constructed for solving the linear operator equation $mathcal{A}(X)=B$‎ ‎and the minimum Frobenius norm residual problem $||mathcal{A}(X)-B||_F$‎ ‎where $Xin mathcal{S}:={Xin textsf{R}^{ntimes n}~|~X=mathcal{G}(X)}$‎, ‎$mathcal{F}$ is the linear operator from $textsf{R}^{ntimes n}$ onto $textsf{R}^{rtimes s}$‎, ‎$ma...

متن کامل

A Smoothing Technique for the Minimum Norm Solution of Absolute Value Equation

One of the issues that has been considered by the researchers in terms of theory and practice is the problem of finding minimum norm solution. In fact, in general, absolute value equation may have infinitely many solutions. In such cases, the best and most natural choice is the solution with the minimum norm. In this paper, the minimum norm-1 solution of absolute value equation is investigated. ...

متن کامل

Iterative solutions to the linear matrix equation

In this paper the gradient based iterative algorithm is presented to solve the linear matrix equation AXB +CXD = E, where X is unknown matrix, A,B,C,D,E are the given constant matrices. It is proved that if the equation has a solution, then the unique minimum norm solution can be obtained by choosing a special kind of initial matrices. Two numerical examples show that the introduced iterative a...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2018