Minimize function with multiple variables with absolute value

Hello,

I have a function minimize

 f(x1,x2,...,xn) = [d1*x1 + d2*x2 + ... + dn*xn] + [abs(x1) + abs(x2) + .... + abs(xn)] * e

( d and e is known)

with constrains A * x <= b.

Without the second part with absolute value of x, I can use intlinprog function and it works well.

Do you have any suggestion for the solution of minimize f ?

Thank you.

Answer 1

[Matt J]

If e is positive, rewrite this as a linear program with additional unknowns ,