
From:  Jared Miller 
Subject:  [Helpglpk] C API: Setting up a leastabsolutedeviation problem 
Date:  Fri, 31 Aug 2012 15:52:11 0700 
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 
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