Recently, Mohammad-Nezhad and Terlaky studied the identification of the optimal partition for semidefinite optimization. An approximation of the optimal partition was obtained from a bounded sequence of solutions on, or in a neighborhood of the central path. Here, we use the approximation of the optimal partition in a rounding procedure to generate an approximate maximally complementary solution. The procedure generates a rounded primal-dual solution from an interior solution, sufficiently close to the optimal set, by solving two least square problems.
Technical report 17T-009, Industrial and Systems Engineering, Lehigh University, May 28, 2017