$$\mathbf {2\times 2}$$-Convexifications for convex quadratic optimization with indicator variables

Abstract In this paper, we study the convex quadratic optimization problem with indicator variables. For $${2\times 2}$$ 2 × case, describe hull of epigraph in original space variables, and also give a conic extended formulation. Then, using description for case as building block, derive an SDP relaxation general case. This new formulation is stronger than other relaxations proposed literature problem, including optimal perspective rank-one relaxation. Computational experiments indicate that formulations are quite effective reducing integrality gap problems.