Review on Reformulation of the Mean-Variance Model with Real-life Trading Restrictions

In this paper, we consider a class of portfolio selection problems with cardinality and minimum buy-in threshold constraints in real-life which can be formulated as mixed-integer quadratic programming (MIQP). Two reformulation methods that generate the same tight continuous relaxation of original problem are compared in the context under the branch-and-bound algorithm, one is the Perspective Reformulation and another is the Lift-and-Convexification Reformulation (LCR). Computational results show that the (PC) is more competitive than the (LCR) method in terms of computing time and nodes in MIQP solver CPLEX 12.7, what's more, this outperformance becomes more obvious as the size of instances grows.