Pure Cutting‐Plane Algorithms and their Convergence

Cutting-plane methods solve a mixed-integer program (MIP) by iteratively adding a valid linear inequality that violates a fractional solution of a linear relaxation of the problem. This article surveys cutting-plane algorithms for different subclasses of MIPs and addresses whether these algorithms converge to an optimal solution of MIP in finitely many steps. Keywords: cutting-plane algorithm; convergence; integer programming

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