MIQP

Mixed-Integer Quadratic Problems (MIQP)

$\mathbf{\frac{1}{2} x^T Hx + f^T x \rightarrow min}$

subjected to

$\mathbf{lb \le x \le ub}$

$\mathbf{A x \le b}$

$\mathbf{A_{eq} x = b_{eq}}$

$\mathbf{\forall i \in intVars: x_i \in N}$

Available MIQP solvers: currently only cplex (license: commercial / full version free for educational / free 90-days trial with limitations nVars/nConstraints up to 500), convex problems only (for non-convex MIQCQP you could use interalg)
FuturePlans: Bonmin, Couenne (license: CPL), maybe GUROBI (commercial)

See also: QP, QCQP, MIQCQP, SOCP, SDP