Contents (Sommaire) Combining Approaches to Improve Bounds on Convex Quadratic MINLP Problems

Bounds on the optimal value of a convex 0-1 quadratic programming problem with linear constraints can be improved by a preprocessing step that adds to the quadratic objective function terms which are equal to 0 for all 0-1 feasible solutions yet increase its continuous minimum. The continuous and the CHR bounds are improved if one first uses Plateau’s QCR method (2005), or one of its predecessors, the eigenvalue method of Hammer and Rubin (1970) and the method of Billionnet and Elloumi (2007). We present some preliminary results for convex GQAP problems using the eigenvalue method of Hammer and Rubin.