Supermodularity and valid inequalities for quadratic optimization with indicators

Abstract We study the minimization of a rank-one quadratic with indicators and show that underlying set function obtained by projecting out continuous variables is supermodular. Although supermodular is, in general, difficult, specific for can be minimized linear time. convex hull epigraph from inequalities lifting them into nonlinear original space variables. Explicit forms convex-hull description are given, both an extended formulation via conic quadratic-representable inequalities, along polynomial separation algorithm. Computational experiments indicate lifted form quite effective reducing integrality gap optimization indicators.