Let (a1, b1),..., (an, bn) be n points in the plane R2. Supopse we are trying to find a line L with equation y = ax + ẞ, such that the sum of the vertical distances from the points. (ai, bi) to L is minimized. We set up the following piecewise linear convex problem: n min|aar + B = bi| α,β i=1 Note that here a, ẞ are the variables and that they are free variables.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(a) Write this problem as a linear programming problem. Hint: you should have (free) variables.

Let (a1, b1),..., (an, bn) be n points in the plane R2. Supopse we are trying to find a line
L with equation y = ax + ẞ, such that the sum of the vertical distances from the points.
(ai, bi) to L is minimized. We set up the following piecewise linear convex problem:
n
min|aar + B = bi|
α,β
i=1
Note that here a, ẞ are the variables and that they are free variables.
Transcribed Image Text:Let (a1, b1),..., (an, bn) be n points in the plane R2. Supopse we are trying to find a line L with equation y = ax + ẞ, such that the sum of the vertical distances from the points. (ai, bi) to L is minimized. We set up the following piecewise linear convex problem: n min|aar + B = bi| α,β i=1 Note that here a, ẞ are the variables and that they are free variables.
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