On branching rules for convex mixed-integer nonlinear optimization

Authors:
Pierre Bonami;Jon Lee;Sven Leyffer;Andreas Wächter
Affiliations:
CNRS, Université Aix Marseille, Marseille, France;University of Michigan, MI, USA;Argonne National Laboratory, IL, USA;Northwestern University, Evanston, IL, USA
Venue:
Journal of Experimental Algorithmics (JEA)
Year:
2013

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Abstract

Branch-and-Bound (B&B) is perhaps the most fundamental algorithm for the global solution of convex Mixed-Integer Nonlinear Programming (MINLP) problems. It is well-known that carrying out branching in a nonsimplistic manner can greatly enhance the practicality of B&B in the context of Mixed-Integer Linear Programming (MILP). No detailed study of branching has heretofore been carried out for MINLP. In this article, we study and identify useful sophisticated branching methods for MINLP, including novel approaches based on approximations of the nonlinear relaxations by linear and quadratic programs.