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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 provenefficient in solving MIQP, and the key to the success of an OA algorithm is thestrength of the cutting planes employed. In this paper, we propose a newtechnique for deriving cutting planes for MIQP from various convex relaxations,and, as a result, we develop new OA algorithms for solving MIQP at scale. Thecontributions of our work are two-fold: (1) we bridge the work on theconvexification of MIQP and the algorithm design to solve large-scale problems,and (2) we demonstrate through a computational study on the sparse portfolioselection problem that our algorithms give rise to significant speedupscompared with the state-of-the-art methods in the literature.

An Outer Approximation Method for Solving Mixed-Integer Convex Quadratic Programs with Indicators