Although a variety of algorithms for discrete nonlinear programming have been proposed, the solution of discrete optimization problems is far from mature relative to continuous optimization. This paper focuses on the recursive quadratic programming strategy which has proven to be efficient and robust for continuous optimization. The procedure is adapted to handle problems of mixed discrete nonlinear programming and utilizes the analytical properties of functions and constraints. This first part of the paper considers definitions, concepts and convergence criteria. Part II includes the development and testing of the algorithm.