Extended Formulations for MINLP Problems by Value Decompositions (original) (raw)

1. Abstract Successful mixed integer nonlinear programming algorithms rely on computing tight over- and under- estimators for nonlinear functions. With the advances of mixed integer linear programming, polyhedral approximations over subregions of the original feasible domain have proven to be a successful tool in recent years. Of course, the smaller such a subregion, the tighter a polyhedral approximation can be made, but at the expense of considering many additional subregions. We propose to design polyhedral approximations by taking into account subdivisions of the value range, i.e., the image of the nonlinear function. This may yield a much lower number of subdivisions, if the value range is small. At the same time it serves to classify subdivisions of the domain by similar values, which helps branch-and-bound based solvers avoiding symmetric branches, or, equivalently, improves MILP-based reformulations. The value based decomposition can be formalized as an extended formulation ...