The paper deals with a framework of decomposition schemes, using general mathematical programming duality. This provides for a global optimization approach. In most applications, the qualitative modeling of decision making in a hierarchical structure is done using linear programming. A more general framework is developed by replacing the linear programming duality with general mathematical programming duality. In the paper, first, basic mathematical programming duality results are established. This is followed by the discussion of a basic decomposition scheme based on a simple max-min model. As a particular case, the decomposition of a general mathematical programming model with two sets of variables is described. Also, an economic interpretation in the context of hierarchical planning is provided.