Monday, 16:15 - 16:40 h, Room: H 2032

 

Oktay Günlük
Lattice-free sets, branching disjunctions, and mixed-integer programming

Coauthors: Sanjeeb Dash, Neil B. Dobbs, Tomasz J. Nowicki, Grzegorz M. Swirszcz

 

Abstract:
We study the relationship between valid inequalities for mixed-integer sets, lattice-free sets associated with these inequalities and structured disjunctive cuts, especially the t-branch split cuts introduced by Li and Richard (2008).
By analyzing n-dimensional lattice-free sets, we prove that every facet-defining inequality of the convex hull of a mixed-integer polyhedral set with n integer variables is a t-branch split cut for some positive integer t.
Moreover, this number t does not depend on the data defining the polyhedral set and is bounded by a function of the dimension n only.
We use this result to give a finitely convergent cutting-plane algorithm to solve mixed-integer programs.
We also show that the minimum value t, for which all facets of polyhedral mixed-integer sets with n integer variables
can be expressed as t-branch split cuts, grows exponentially with n. In particular, when n=3, we observe that not all facet-defining inequalities are 6-branch split cuts.

 

Talk 3 of the invited session Mon.3.H 2032
"Trends in mixed integer programming I" [...]
Cluster 11
"Integer & mixed-integer programming" [...]

 

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