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 descrip...

Recent advances on the understanding of valid inequalities from the infinite group relaxation has opened the possibility of finding a computationally effective extension to GMI cuts. In this paper, we investigate the computational impact of using a subclass of minimally-valid inequalities from this relaxation on a wide set of instances.

The trust-region subproblem minimizes a general quadratic function over an ellipsoid and can be solved in polynomial time using a semidefinite-programming (SDP) relaxation. Intersecting the feasible set with a second ellipsoid results in the two-trust-region subproblem (TTRS). Even though TTRS can also be solved in polynomial-time, existing algorithms do not use SDP. In this paper, we investiga...