AN EFFICIENT PARAMETERIZED LOGARITHMIC KERNEL FUNCTION FOR SEMIDEFINITE OPTIMIZATION

摘要

In this work, we propose a primal-dual interior point algorithm for semidefinite optimization SDO based on a new kernel function with an efficient logarithmic barrier term. We show that the best result of iteration bounds can be achieved, namely 0(root nlog n log n/epsilon) for large-update and O(root nlog n/epsilon) for small-update methods, which improves significantly the so far obtained complexity results based on a logarithmic kernel function for SDO namely 0(n log for large-update and 0(root nlog n/epsilon) for small-update methods. Some numerical tests are reported to show the efficiency of the algorithm.