  We investigate a mixed 0-1 conic quadratic optimization problem with
indicator variables arising in mean-risk optimization. The indicator variables
are often used to model non-convexities such as fixed charges or cardinality
constraints. Observing that the problem reduces to a submodular function
minimization for its binary restriction, we derive three classes of strong
convex valid inequalities by lifting the polymatroid inequalities on the binary
variables. Computational experiments demonstrate the effectiveness of the
inequalities in strengthening the convex relaxations and, thereby, improving
the solution times for mean-risk problems with fixed charges and cardinality
constraints significantly.
