Linearization

In http://yetanothermathprogrammingconsultant.blogspot.com/2012/09/bi-criteria-optimization.html I discussed an algorithm to trace the efficient frontier. We solve a number of non-convex MINLP’s for this. It is fairly easy to linearize the quadratic function by observing that the z_k's only assume discrete values 0,1,..,c_p.I used something like:

 

The MIP formulation seems to perform a little bit better even though the model size (in terms of variables and equations) increases significantly:

Note: the size of the problems increases for each new non-dominated point. We give here the smallest (i.e. first) problem size and the largest (i.e. last) one.