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all,

I met a question that, the cost function of the linear programming problem is a function with absolute value. Here is the problem:

min 3x1+|6x2+3|
st. |x1+4|+|2x2|<=3

How can I deal with it?

Thank you!

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1 Answer 1

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Replace $|6 x_2 + 3|$ by a new variable $x_3$ with $x_3 \le 6 x_2 + 3$ and $x_3 \le -(6 x_2 + 3)$. Similarly your constraint becomes four constraints $\pm (x_1 + 4) \pm (2 x_2) \le 3$.

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