The tables below show the performance of the algorithms discussed in Section 2 and 3 on the first eight SDP examples described in Section 6. The result for each example is based on ten random instances with normally distributed data generated via the MATLAB command randn. The initial iterate for each problem is infeasible, generated from infeaspt.m with the default option. Note that the same set of random instances is used throughout for each example.
In Tables 2 and 3, we use the default value (given in Section 5) for the parameters used in the algorithms.
In our experiments, we consider an SDP instance successfully solved by Algorithm IPC if the algorithm manages to reduce the relative duality gap to less than while at the same time the infeasibility measure is less than the relative duality gap. For Algorithm HPC, we consider an SDP instance successfully solved if the relative duality gap is less than while the infeasibility measure is at most 5 times more than the relative duality gap.
All of the SDP instances (a total of 640) considered in our experiments were successfully solved, except for only three ETP instances and one Logarithmic Chebyshev instance where Algorithm HPC using the AHO direction failed. This indicates that our algorithms are probably quite robust.
The results in Tables 2 and 3 show that the behavior of Algorithm IPC and HPC are quite similar in terms of efficiency (number of iterations) and accuracy on all the the four search directions we implemented. For both algorithms, the AHO and GT directions are more efficient and more accurate than the HKM and NT directions, with the former and latter pairs having similar behavior in terms of efficiency and accuracy.