Abstract.
We study the mixed 0-1 knapsack polytope, which is defined by a single knapsack constraint that contains 0-1 and bounded continuous variables, through the lifting of continuous variables fixed at their upper bounds. We introduce the concept of a superlinear inequality and show that, in this case, lifting is significantly simpler than for general inequalities. We use the superlinearity theory, together with the traditional lifting of 0-1 variables, to describe families of facets of the mixed 0-1 knapsack polytope. Finally, we show that superlinearity results can be extended to nonsuperlinear inequalities when the coefficients of the variables fixed at their upper bounds are large.
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This research was supported by NSF grants DMI-0100020 and DMI-0121495
Mathematics Subject Classification (1991): 90C11, 90C27
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Richard, JP., de Farias Jr, I. & Nemhauser, G. Lifted inequalities for 0-1 mixed integer programming: Superlinear lifting. Math. Program., Ser. B 98, 115–143 (2003). https://doi.org/10.1007/s10107-003-0399-1
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DOI: https://doi.org/10.1007/s10107-003-0399-1