  The mean and variance of portfolio returns are the standard quantities to
measure the expected return and risk of a portfolio. Efficient portfolios that
provide optimal trade-offs between mean and variance warrant consideration. To
express a preference among these efficient portfolios, investors have put
forward many mean-variance portfolio (MVP) formulations which date back to the
classical Markowitz portfolio. However, most existing algorithms are highly
specialized to particular formulations and cannot be generalized for broader
applications. Therefore, a fast and unified algorithm would be extremely
beneficial. In this paper, we first introduce a general MVP problem formulation
that can fit most existing cases by exploring their commonalities. Then, we
propose a widely applicable and provably convergent successive quadratic
programming algorithm (SCQP) for the general formulation. The proposed
algorithm can be implemented based on only the QP solvers and thus is
computationally efficient. In addition, a fast implementation is considered to
accelerate the algorithm. The numerical results show that our proposed
algorithm significantly outperforms the state-of-the-art ones in terms of
convergence speed and scalability.
