The theory of self-concordance, initiated by Nesterov and Nemirovskii, has become very popular in recent years. In this paper an lnν reduction of the complexity is given for finding the analytical center for a ν-self-concordant barrier. This center-finding step is a crucial one in the primal self-concordant barrier method.

Algorithm, Analytical center, Barrier method, Complexity, Interior point methods, Optimization, Primal path-following methods, Self-concordance,
Operations Research Letters
Erasmus School of Economics

Brinkhuis, J. (2003). On the complexity of the primal self-concordant barrier method. Operations Research Letters, 31(6), 442–444. doi:10.1016/S0167-6377(03)00056-7