Subadditive Approaches to Mixed Integer Programming

Moazzez, Babak

doi:10.22215/etd/2014-10380

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Data Mixed Integer Linear Program Min{1

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“…In [16], it is shown that if we have a branch and bound tree instead of a set of cutting planes, we can still get the cutting planes that we need from the tree. This is done by using two different families of cuts, namely, infeasibility cuts (extracted from an infeasible node of the tree) and disjunctive cuts (extracted from a disjunction of the tree or a branch).…”

Section: Data Mixed Integer Linear Program Min{mentioning

confidence: 99%

Certificates of Optimality for Mixed Integer Linear Programming Using Generalized Subadditive Generator Functions

Cheung

Moazzez²

2016

Advances in Operations Research

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We introduce generalized subadditive generator functions for mixed integer linear programs. Our results extend Klabjan’s work from pure integer programs with nonnegative entries to general MILPs. These functions suffice to achieve strong subadditive duality. Several properties of the functions are shown. We then use this class of functions to generate certificates of optimality for MILPs. We have performed a computational test study on knapsack problems to investigate the efficiency of the certificates.

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Section: Data Mixed Integer Linear Program Min{mentioning

confidence: 99%