Improving the Approximated Projected Perspective Reformulation by dual information

We propose an improvement of the Approximated Projected Perspective Reformulation (APR) for dealing with constraints linking the binary variables. The new approach solves the Perspective Reformulation (PR) once, and then use the corresponding dual information to reformulate the problem prior to applying APR, thereby combining the root bound quality of the PR with the reduced relaxation computing time of APR. Computational results for the cardinality-constrained Mean-Variance portfolio optimization problem show that the new approach is competitive with state-of-the-art ones.