Solving Using Linear Programming
The problem can be solved using any linear programming technique on the following problem specification. We wish to
with respect to the choice of the values of the parameters, where yi is the value of the ith observation of the dependent variable, and xij is the value of the ith observation of the jth independent variable (j = 1,...,k). We rewrite this problem in terms of artificial variables ui as
- with respect to and
- subject to
These constraints have the effect of forcing each to equal upon being minimized, so the objective function is equivalent to the original objective function. Since this version of the problem statement does not contain the absolute value operator, it is in a format that can be solved with any linear programming package.
Read more about this topic: Least Absolute Deviations, Solving Methods
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