Equivariant Perturbation in Gomory and Johnson’s Infinite Group Problem. Vi. the Curious Case of Two-sided Discontinuous Functions
نویسندگان
چکیده
We construct a two-sided discontinuous piecewise linear minimal valid function for the 1-row Gomory–Johnson model which is not extreme, but which is not a convex combination of other piecewise linear minimal valid functions. This anomalous behavior results from combining features of Hildebrand’s two-sided discontinuous extreme functions and Basu–Hildebrand–Köppe’s piecewise linear extreme function with irrational breakpoints, . The new function only admits piecewise microperiodic perturbations. We present an algorithm for computations with a restricted class of such perturbations.
منابع مشابه
Equivariant Perturbation in Gomory and Johnson’s Infinite Group Problem. Vi. the Curious Case of Two-sided Discontinuous Minimal Valid Functions
We construct a two-sided discontinuous piecewise linear minimal valid cut-generating function for the 1-row Gomory–Johnson model which is not extreme, but which is not a convex combination of other piecewise linear minimal valid functions. The new function only admits piecewise microperiodic perturbations. We present an algorithm for verifying certificates of non-extremality in the form of such...
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