  Mixed-integer convex quadratic programs with indicator variables (MIQP)
encompass a wide range of applications, from statistical learning to energy,
finance, and logistics. The outer approximation (OA) algorithm has been proven
efficient in solving MIQP, and the key to the success of an OA algorithm is the
strength of the cutting planes employed. In this paper, we propose a new
technique for deriving cutting planes for MIQP from various convex relaxations,
and, as a result, we develop new OA algorithms for solving MIQP at scale. The
contributions of our work are two-fold: (1) we bridge the work on the
convexification of MIQP and the algorithm design to solve large-scale problems,
and (2) we demonstrate through a computational study on the sparse portfolio
selection problem that our algorithms give rise to significant speedups
compared with the state-of-the-art methods in the literature.
