Author/Authors :
Bai، Y.Q.. نويسنده Department of Mathematical Sciences, Shanghai University, Shanghai, China. , , Lesaja، G. نويسنده Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA 30460-8093, U.S.A. , , Mansouri، H. نويسنده Department of Applied Mathematics, Shahrekord University, P.O. Box 115, Shahrekord, Iran. , , Roos، C. نويسنده Department of Software Technology and Algorithms, Delft University of Technology, P. O. Box 5031, 2600, Delft, The Netherlands. , , Zangiabadi، M. نويسنده Department of Applied Mathematics, Shahrekord University, P.O. Box 115, Shahrekord, Iran. ,
Abstract :
Many efficient interior-point methods (IPMs) are based on the use of a self-concordant barrier
function for the domain of the problem that has to be solved. Recently, a wide class of new barrier
functions has been introduced in which the functions are not self-concordant, but despite this fact
give rise to efficient IPMs. Here, we introduce the notion of locally self-concordant barrier
functions and we prove that the new barrier functions are locally self-concordant. In many cases,
the (local) complexity numbers of the new barrier functions along the central path are better than
the complexity number of the logarithmic barrier function by a factor between 0.5 and 1.
