@article {IOPORT.02247897,
    author       = {Wang, G.Q. and Bai, Y.Q. and Roos, C.},
    title        = {Primal-dual interior-point algorithms for semidefinite optimization based on a simple kernel function.},
    year         = {2005},
    journal      = {JMMA. Journal of Mathematical Modelling and Algorithms [electronic only]},
    volume       = {4},
    number       = {4},
    issn         = {1570-1166},
    pages        = {409-433},
    publisher    = {Springer, Dordrecht},
    doi          = {10.1007/s10852-005-3561-3},
    abstract     = {Summary: Interior-point methods (IPMs) for semidefinite optimization (SDO) have been studied intensively, due to their polynomial complexity and practical efficiency. Recently, J. Peng et al. introduced so-called self-regular kernel (and barrier) functions and designed primal-dual interior-point algorithms based on self-regular proximities for linear optimization (LO) problems. They also extended the approach for LO to SDO. In this paper we present a primal-dual interior-point algorithm for SDO problems based on a simple kernel function which was first presented at the Proceedings of Industrial Symposium and Optimization Day, Australia, November 2002; the function is not self-regular. We derive the complexity analysis for algorithms based on this kernel function, both with large- and small-updates. The complexity bounds are $O(qn)\log\frac{n}{\varepsilon}$ and $O(q^{2}\sqrt{n})\log\frac{n}{\varepsilon}$, respectively, which are as good as those in the linear case.},
    identifier   = {02247897},
}