Effective Separation of Disjunctive Cuts for Convex Mixed Integer Nonlinear Programs
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Date
2010Author
Kilinc, Mustafa
Linderoth, Jeff
Luedtke, James
Publisher
University of Wisconsin-Madison Department of Computer Sciences
Metadata
Show full item recordAbstract
We describe a computationally effective method for generating
disjunctive inequalities for convex mixed-integer nonlinear programs
(MINLPs). The method relies on solving a sequence of cut-generating
linear programs, and in the limit will generate an inequality as
strong as can be produced by the cut-generating nonlinear program
suggested by Stubbs and Mehrotra. Using this procedure, we are able
to approximately optimize over the rank one simple disjunctive closure
for a wide range of convex MINLP instances. The results indicate that
disjunctive inequalities have the potential to close a significant
portion of the integrality gap for convex MINLPs. In addition, we
find that using this procedure within a branch-and-cut solver for
convex MINLPs yields significant savings in total solution time for
many instances. Overall, these results suggest that with an effective
separation routine, like the one proposed here, disjunctive
inequalities may be as effective for solving convex MINLPs as they
have been for solving mixed-integer linear programs.
Permanent Link
http://digital.library.wisc.edu/1793/60720Citation
TR1681