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Linearization Strategies for a Class of Zero-One Mixed Integer Programming Problems

This paper is concerned with a new linearization strategy for a class of zero-one mixed integer programming problems that contains quadratic cross-product terms between continuous and binary variables, and between the binary variables themselves. This linearization scheme provides an equivalent mixed integer linear programming problem which yields a tighter continuous relaxation than that obtainable via the alternative linearization techniques available in the literature. Moreover, the proposed technique provides a unifying framework in the sense that all the alternate methods lead to formulations that are accessible through appropriate surrogates of the constraints of the new linearized formulation. Extensions to various other types of mixed integer nonlinear programming problems are also discussed.