Journal Article10.1287/OPRE.18.3.404
Cutting-plane methods without nested constraint sets
TL;DR: General conditions for the convergence of a class of cutting-plane algorithms without requiring that the constraint sets for the sub-problems be sequentially nested are given.
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Abstract: This paper gives general conditions for the convergence of a class of cutting-plane algorithms without requiring that the constraint sets for the sub-problems be sequentially nested. Conditions are given under which inactive constraints may be dropped after each subproblem. Procedures for generating cutting-planes include those of Kelley, Cheney and Goldstein, and a generalization of the one used by both Zoutendijk and Veinott. For algorithms with nested constraint sets, these conditions reduce to a special case of those of Zangwill for such problems and include as special cases the algorithms of Kelley, Cheney and Goldstein, and Veinott. Finally, the paper gives an arithmetic convergence rate.
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Citations
An outer-approximation algorithm for a class of mixed-integer nonlinear programs
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References
•Book
Linear Programming and Extensions
George B. Dantzig
- 01 Jan 1963
TL;DR: This classic book looks at a wealth of examples and develops linear programming methods for their solutions and begins by introducing the basic theory of linear inequalities and describes the powerful simplex method used to solve them.
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