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.

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doi.org/10.1016/S0167-6377(03)00056-7, hdl.handle.net/1765/69328
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