@misc{nin-mes-11-aa-mixglob,
  author = {Jordan Ninin and Fr{\'e}d{\'e}ric Messine},
  title = {A Mixed Integer Affine Reformulation Technique for Deterministic Global Optimization},
  url = {https://www.researchgate.net/publication/228573281_A_Mixed_Integer_Affine_Reformulation_Technique_for_Deterministic_Global_Optimization},
  howpublished = {Online document},
  year = 2011,
  month = mar,
  altkeys = {nin-mes-12-aa-mixglob},
  comment = {See also~\cite{nin-mes-10-aa-globopt}. Date inferred from PDF metadata.},
  abstract = {Since few years, the methods to solve mixed integer non-linear programming (MINLP) problems has made some breakthroughs. It is now possible to consider very difficult and large problems. One of these improvements is the growing use of relaxation techniques. The most famous one is the convex relaxation based on the symbolic reformulation introduced by Smith and Pantelides [5]. This reformulation is performed by introducing a new variable for every non-convex operators. Our approach is different. The method is based on a relaxation technique using the affine arithme-tic, which does not introduce new variable [4]. We will present an extension of this new technique to consider integer variables to reformulate a MINLP problem into a mixed integer linear program (MILP) which keeps the same size as the original one. This relaxation is used in Branch and Bound algorithm based on interval analysis to compute lower bound and eliminate sub-domains which do not contain the global minimum.}
}