A primal-dual large-update interior-point algorithm for semi-definite optimization based on a new kernel function

Abstract

Based on a new parametric kernel function, this paper presents a primal-dual large-update interior-point algorithm (IPM) for semi-definite optimization (SDO) problems. The new parametric function is neither self-regular function nor the usual logarithmic barrier function.  It is strongly convex and possesses some novel  analytic properties. We analyse this new parametric kernel function and show that the proposed algorithm has favorable complexity bound in terms of the analytic properties of the kernel function. Moreover, the complexity bound for our large-update IPM is shown to be O(\sqrt{n}(\log n)^2 \log\frac{n}{\epsilon}). Some numerical results are reported to illustrate the feasibility of the proposed algorithm.