A type calculus for mathematical programming modeling languages

Abstract

The issue of model validation is critical in the formulation and interpretation of mathematical programming models, yet this problem is largely ignored by contemporary modeling languages and the systems they support. This research advanced modeling languages for mathematical programming by providing a formalism and defining a language for specifying a dimensional complement, called typing, to the algebraic representation of models. Typing is a formal specification used to determine automatically whether the algebraic model is well-formed in the sense that its objective junction and constraints are composed of homogeneous components and that operations junction and constraints are composed of homogeneous components and that operations performed using indices are meaningful. A provision is made for the definition of dimensional axioms that can be applied automatically to resolve dimensional differences. The addiction of formal typing to mathematical programming models also yields a powerful abstraction mechanism for integrated modeling.