An Efficient Parameterized Logarithmic Kernel Function for Semidefinite Optimization

In this paper, we present a primal-dual interior point algorithm for semidefinite optimization problems based on a new class of kernel functions. These functions constitute a combination of the classic kernel function and a barrier term.We derive the complexity bounds for large and small-update methods respectively. We show that the best result of iteration bounds for large and small-update methods can be achieved, namely O(qn(logn)/q logn/ε)for large-update methods and O(q(logq)/q nlogn/ε) for small-update methods.We test the efficiency and the validity of our algorithm by running some computational tests, then we compare our numerical results with results obtained by algorithms based on different kernel functions.