On the convex hull of convex quadratic optimization problems with indicators. (arXiv:2201.00387v1 [math.OC])

We consider the convex quadratic optimization problem with indicator
variables and arbitrary constraints on the indicators. We show that a convex
hull description of the associated mixed-integer set in an extended space with
a quadratic number of additional variables consists of a single positive
semidefinite constraint (explicitly stated) and linear constraints. In
particular, convexification of this class of problems reduces to describing a
polyhedral set in an extended formulation. We also give descriptions in the
original space of variables: we …

arxiv math optimization quadratic optimization