In this chapter we study in detail the class of hypermetric inequalities. In particular, we present several subclasses of hypermetric inequalities that define facets of the cut cone. We also address the separation problem for hypermetric inequalities. Although its exact complexity status is not known, there are several results that indicate that it is very likely to be a hard problem. In particular, the problem of finding the smallest violated hypermetric inequality is NP-hard.
KeywordsConvex Body Positive Semidefinite Valid Inequality Separation Problem Positive Semidefinite Matrix
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