A level set approach to integer nonlinear optimization

Integer nonlinear optimization programs form a class of very hard problems. Often it is much easier to solve the continuous relaxation. Therefore we are interested in this thesis in identifying special cases of integer nonlinear optimization problems where an optimal solution to the integer problem can be found by rounding the components of an optimal solution to the continuous relaxation. We identify those special cases by the shape of the interesection of the level sets of the objective function and the feasible region