Algorithms for general 0-1 mixed integer programs can be successfully developed by using lift-and-project methods to generate cuts. Cuts are generated by solving a cut- generation-program that depends on a certain normalization. From a theoretical point of view, the good numerical behavior of these cuts is not completely understood yet, specially, concerning to the normalization chosen. We consider a general normalization given by an arbitrary closed convex set, extending the theory developed in the 90's. We present a theoretical framework covering a wide group of already known normalizations. We also introduce new normalizations and analyze the properties of the associated cuts. In this work, we also propose a new updating rule for the prox parameter of a variant of the proximal bundle methods, making use of all the information available at each iteration. Proximal bundle methods are well known for their efficiency in nondifferentiable optimization. Finally, we introduce a way to eliminate redundant solutions ( due to geometrical symmetries ) of combinatorial integer program. This can be done by using the information about the problem symmetry in order to generate inequalities, which added to the formulation of the problem, eliminate this symmetry without affecting solution of the integer problem.