 
Summary: BCOL RESEARCH REPORT 06.03
Industrial Engineering & Operations Research
University of California, Berkeley, CA
Forthcoming in Mathematical Programming
CONIC MIXEDINTEGER ROUNDING CUTS
ALPER ATAMTšURK AND VISHNU NARAYANAN
Abstract. A conic integer program is an integer programming problem with
conic constraints. Many problems in finance, engineering, statistical learning,
and probabilistic optimization are modeled using conic constraints.
Here we study mixedinteger sets defined by secondorder conic constraints.
We introduce generalpurpose cuts for conic mixedinteger programming based
on polyhedral conic substructures of secondorder conic sets. These cuts can be
readily incorporated in branchandbound algorithms that solve either second
order conic programming or linear programming relaxations of conic integer
programs at the nodes of the branchandbound tree.
Central to our approach is a reformulation of the secondorder conic con
straints with polyhedral secondorder conic constraints in a higher dimensional
space. In this representation the cuts we develop are linear, even though they
are nonlinear in the original space of variables. This feature leads to a com
putationally efficient implementation of nonlinear cuts for conic mixedinteger
