What is the most efficient way to solve linear Least absolute deviation regression problem?

I know it can be solved using linear programming, is there a better/faster method?

Edit: I'm interested in the more theoretical aspect, hence by "efficient" I mean that it have some type of upper bound on its run-time.

  • $\begingroup$ If you are going to use a non-linear solver such as Levenberg-Marquardt or Gradient Descent, you will need good initial parameter estimates for the solver. If you can use standard OLS to get the sum-of-squared-error solution, this is usually close to the LAD solution and can be used as initial parameter estimates. $\endgroup$ – James Phillips Feb 10 '19 at 21:35
  • $\begingroup$ Is your answer based on rigorous bounds for the running time or by empirical observations? $\endgroup$ – Meni Feb 11 '19 at 4:58
  • 1
    $\begingroup$ My comment was intended as a potentially helpful suggestion regarding initial parameter estimates only. $\endgroup$ – James Phillips Feb 11 '19 at 9:45

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