Branching on hyperplane methods for mixed integer linear and convex programming using adjoint lattices

Sanjay Mehrotra*, Zhifeng Li

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


We present branching-on-hyperplane methods for solving mixed integer linear and mixed integer convex programs. In particular, we formulate the problem of finding a good branching hyperplane using a novel concept of adjoint lattice. We also reformulate the problem of rounding a continuous solution to a mixed integer solution. A worst case complexity of a Lenstra-type algorithm is established using an approximate log-barrier center to obtain an ellipsoidal rounding of the feasible set. The results for the mixed integer convex programming also establish a complexity result for the mixed integer second order cone programming and mixed integer semidefinite programming feasibility problems as a special case. Our results motivate an alternative reformulation technique and a branching heuristic using a generalized (e.g., ellipsoidal) norm reduced basis available at the root node.

Original languageEnglish (US)
Pages (from-to)623-649
Number of pages27
JournalJournal of Global Optimization
Issue number4
StatePublished - Apr 2011


  • Analytic center
  • Convex programming
  • Interior point methods
  • Lattice basis reduction
  • Linear programming
  • Mixed integer programming
  • Volumetric center

ASJC Scopus subject areas

  • Computer Science Applications
  • Management Science and Operations Research
  • Control and Optimization
  • Applied Mathematics


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