Part II General Integer Programming II.1 The Theory of Valid Inequalities 1

Integer Programming

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Integer Rounding Integer Programming

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Chvatal-Gomory (C-G) Rounding Method Integer Programming

Optimizing over the First Chvátal closure Integer Programming

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 If we find good but not necessarily optimal solutions to the MIP, we find very effective valid inequalities. Also heuristic methods to find good feasible solutions to the MIP are helpful.  MIP model may not be intended as computational tools to solve real problems. But we can examine the strength of rank-1 C-G inequalities to describe the convex hull of S for various problems.  For some structured problems, e.g. knapsack problem, the separation problem for the first Chvatal closure may have some structure which enables us to handle the problem more effectively. Integer Programming

Modular Arithmetic Integer Programming

Disjunctive Constraints Integer Programming

Integer Programming

Integer Programming

Boolean Implications Integer Programming

Geometric or Combinatorial Implication Integer Programming