If the quadratic function is convex (i.e., the Hessian is positive definite or positive semidefinite), the solution obtained will be a global minimizer. If the quadratic is non-convex (i.e., the Hessian is indefinite), the solution obtained will be a local minimizer or a dead-point.
A two-phase active-set method is used. The first phase minimizes the sum of infeasibilities. The second phase minimizes the quadratic function within the feasible region, using a reduced Hessian to obtain search directions. The method is most efficient when many constraints or bounds are active at the solution.
QPOPT is not intended for large sparse problems, but there is no fixed limit on problem size.