Generating Valid Inequalities and Facets Using RLT
Thus far, we have presented a hierarchy of relaxations leading up to the convex hull representation for zero-one mixed-integer programming problems, and have developed extensions of this hierarchy to accommodate inherent special structures as well as to handle general discrete (as opposed to simply 0–1) variables. A key advantage of this development that we wish to discuss in the present chapter is that the RLT produces an algebraically explicit convex hull representation at the highest level. While it might not be computationally feasible to actually generate and solve the linear program based on this convex hull representation because of its potentially exponential size, there are other ways to exploit this information or facility to advantage as we shall presently see.
KeywordsValid Inequality Polyhedral Cone Basic Feasible Solution Nonnegativity Constraint Extreme Direction
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