Valid inequalities based on the interpolation procedure

Valid inequalities based on the interpolation procedure

We study the interpolation procedure of Gomory and Johnson (1972), which generates cutting planes for general integer programs from facets of cyclic group polyhedra. This idea has recently been re-considered by Evans (2002) and Gomory, Johnson and Evans (2003). We compare inequalities generated by this procedure with mixed-integer rounding (MIR) based inequalities discussed in Dash and Gunluk (...

Notes on Interpolation Inequalities

Valid Inequalities Based on Simple Mixed-Integer Sets

In this paper we use facets of simple mixed-integer sets with three variables to derive a parametric family of valid inequalities for general mixed-integer sets. We call these inequalities two-step MIR inequalities as they can be derived by applying the simple mixed-integer rounding (MIR) principle of Wolsey (1998) twice. The two-step MIR inequalities define facets of the master cyclic group po...

Generating Minimal Valid Inequalities

We consider the problem of generating a lattice-free convex set to find a valid inequality that minimizes the sum of its coefficients for 2-row simplex cuts. Multi-row simplex cuts has been receiving considerable attention recently and we show that a pseudo-polytime generation of a lattice-free convex set is possible. We conclude with a short numerical study.

Improved interpolation inequalities on the sphere

This paper contains a review of available methods for establishing improved interpolation inequalities on the sphere for subcritical exponents. Pushing further these techniques we also establish some new results, clarify the range of applicability of the various existing methods and state several explicit estimates.