[Help-glpk] C API: Setting up a least-absolute-deviation problem

[Jared Miller]

I have an absolute value objective function, minimizing the sum of abs( s[i] - x[i] ) for two vectors s and x, with the constraints given by Ax = b where A is a large but very sparse matrix.

So I'm using a dummy vector "u" in a MathProg model:

minimize least_abs_dev: sum {i in I} (u[i]);

s.t. constr1{i in I} : b[i] = sum{j in I} (A[i,j] * x[j]);

s.t. constr2{i in I} : u[i] >= (s[i] - x[i]);

s.t. constr3{i in I} : u[i] >= -(s[i] - x[i]);

I also eventually want to incorporate weights into the objective:

minimize least_abs_dev: sum {i in I} (u[i] * w[i]);

I've got this type of model working using MathProg and glpsol, but now I'm trying to figure out how to translate it to the strict form required by the C API. Has anyone done this? What's the best way to go about it? I'm going to need high performance on some large problems.

I am fairly new to optimization and GLPK. Any help would be much appreciated.

- JM