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Linear programming, interested in only 1 variable

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It might be a stupid question, but I'm a bit confused. You have inequalities, want to find the smallest for example value.
So you need to solve s.t. . Calling a solver will give a result with
Is this the correct way to solve it? variable values are meaningless


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Accepted Answer

Bruno Luong
Bruno Luong on 16 Sep 2019
Edited: Bruno Luong on 16 Sep 2019
If you want to minimize x1 under A*x <= b
f = zeros(size(x));
f(1) = 1;
x = linprog(f, A, b);
(x2,...,xn) is not meaningless, it's the associate components such that your constraint A*x <= b is satisfied.
Imagine you want to find most left corner of a 2D triangle.
It can be written as
A*x <= b
with x is 2 x 1, A is 3 x 2, b and 3 x 1.
the LINPROG returns you (x1,x2) coordinates of the left most corner (minimize x1) even if you ignore x2 it's still the ordinate of the corner.

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