Abstract
Any real-valued nonlinear function in 0–1 variables can be rewritten as a multilinear function. We discuss classes of lower and upper bounding linear expressions for multilinear functions in 0–1 variables. For any multilinear inequality in 0–1 variables, we define an equivalent family of linear inequalities. This family contains the well-known system of generalized covering inequalities, as well as other linear equivalents of the multilinear inequality that are more compact, i.e., of smaller cardinality. In a companion paper [7]. we discuss dominance relations between various linear equivalents of a multilinear inequality, and describe a class of algorithms for multilinear 0–1 programming based on these results.
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Research supported by the National Science Foundation under grant ECS7902506 and by the Office of Naval Research under contract N00014-75-C-0621 NR 047-048.
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Balas, E., Mazzola, J.B. Nonlinear 0–1 programming: I. Linearization techniques. Mathematical Programming 30, 1–21 (1984). https://doi.org/10.1007/BF02591796
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DOI: https://doi.org/10.1007/BF02591796