Solving DC programs with a polyhedral component utilizing a multiple   objective linear programming solver
  A class of non-convex optimization problems with DC objective function is studied, where DC stands for being representable as the difference $f=g-h$ of two convex functions $g$ and $h$. In particular, we deal with the special case where one of the two convex functions $g$ or $h$ is polyhedral. In case $g$ is polyhedral, we show that a solution of the DC program can be obtained from a solution of an associated polyhedral projection problem. In case $h$ is polyhedral, we prove that a solution of the DC program can be obtained by solving a polyhedral projection problem and finitely many convex programs. Since polyhedral projection is equivalent to multiple objective linear programming (MOLP), a MOLP solver (in the second case together with a convex programming solver) can be used to solve instances of DC programs with polyhedral component. Numerical examples are provided, among them an application to locational analysis. 
Andreas L\"ohne and Andrea Wagner
math.OC