Outline of an Algorithm for Integer Solutions to Linear Programs and An Algorithm for the Mixed Integer Problem

By R. Gomory. 50 Years of Integer Programming, 2010

531 citations recorded by the source corpus.

How researchers see this paper

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Concave Quadratic Cuts for Mixed-Integer Quadratic Problems (2015, methodology): “Our main idea resembles that of cutting-plane method [Kel60], and is closely related to hierarchies of linear and semidefinite programs suggested by Lovász and Schrijver [LS91], Sherali and Adams [SA90], Gomory [Gom58], Chvátal [Chv73], and Lasserre [Las01a].”
A Primer on Monotone Operator Methods (2015, background): “By judiciously choosing points to evaluate and accumulating the cutting planes, one can localize a small set in which x⋆ must lie in [29,65,68,73,78,91,92,95,107,108].”
Algorithms and Software for Convex Mixed Integer Nonlinear Programs (2012, background): “Gomory Cuts.”
Branch-and-bound algorithms: A survey of recent advances in searching, branching, and pruning (2016, unknown): “The initial cutting planes described by Gomory are called Gomory (mixed integer) cuts, and are based on the structure of the simplex tableau.”