Abstract
A Linear Programme (LP) involves a conjunction of linear constraints and has a well defined dual. It is shown that if we allow the full set of Boolean connectives {∧, ∨, ∼} applied to a set of linear constraints we get a model which we define as a Logical Linear Programme (LLP). This also has a well defined dual preserving most of the properties of LP duality. Generalisations of the connectives are also considered together with the relationship with Integer Programming formulation.
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Williams, H. The Dual of a Logical Linear Programme. Journal of Global Optimization 18, 129–141 (2000). https://doi.org/10.1023/A:1008328500933
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DOI: https://doi.org/10.1023/A:1008328500933