Inequalities from Two Rows of a Simplex Tableau
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Minimal Inequalities for an Infinite Relaxation of Integer Programs
SIAM Journal on Discrete Mathematics
Constrained Infinite Group Relaxations of MIPs
SIAM Journal on Optimization
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In optimization problems such as integer programs or their relaxations, one encounters feasible regions of the form $\{x\in\mathbb{R}_+^n:\: Rx\in S\}$ where R is a general real matrix and S⊂ℝq is a specific closed set with 0∉S. For example, in a relaxation of integer programs introduced in [ALWW2007], S is of the form ℤq−b where $b \not\in \mathbb{Z}^q$. One would like to generate valid inequalities that cut off the infeasible solution x=0. Formulas for such inequalities can be obtained through cut-generating functions. This paper presents a formal theory of minimal cut-generating functions and maximal S-free sets which is valid independently of the particular S. This theory relies on tools of convex analysis.