Although a variety of algorithms for discrete nonlinear programming have been proposed, the solution of discrete optimization problems is far from mature compared to continuous optimization techniques. 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 consider a class of mixed discrete nonlinear programming problems and utilizes the analytical properties of functions and constraints. This first part of the paper considers definitions, concepts, and possible convergence criteria. Part II includes the development and testing of the algorithm.

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