Domain reduction is the process of eliminating regions from the feasible space if the removal does not affect the convergence of the search process to a global optimum. Domain reduction is also referred to as bounds tightening, domain contraction, and range reduction. Various techniques for domain reduction have been developed by Mangasarian & McLinden (1985), Thakur (1990), Hansen, Jaumard & Lu (1991), Hamed & McCormick (1993), Lamar (1993), Savelsbergh (1994), Andersen & Andersen (1995), Ryoo & Sahinidis (1995), Ryoo & Sahinidis (1996), Shectman & Sahinidis (1998), Zamora & Grossmann (1999). We develop a theory of domain reduction in this chapter and then derive earlier results in the light of these new developments. For example, our results generalize to the nonlinear case, range reduction tests used in the integer linear programming literature.
KeywordsMaster Problem Dual Solution Range Reduction Optimal Dual Solution Dualizing Parameterization
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