Kernel function-based primal-dual interior-point methods for symmetric cones optimization

Abstract

In this paper, we present a large-update primal-dual interior-point method for symmetric cone optimization (SCO) based on a new kernel function, which determines both search directions and the proximity measure between the iterate and the center path. The kernel function is neither a self-regular function nor the usual logarithmic kernel function. Besides, by using Euclidean Jordan algebraic techniques, we achieve the favorable iteration complexity \(O(\sqrt r (\log r)^2 \log (r/\varepsilon ))\), which is as good as the convex quadratic semi-definite optimization analogue.