Affine Relaxation Techniques

Since 2007 My main research concerns an automatic method for constructing linear relaxations of global optimization problems with constraints. This construction is based on interval arithmetic and affine arithmetic using operator overloading. The linear problem has generated exactly the same number of variables and inequality constraints that the original problem, each equality constraint is replaced by two inequalities. This new method to compute reliable bounds and certificates of infeasibility is inserted in a classical interval Branch and Bound, named IBBA.