| |
| In this paper, we generalize primal-dual interior-point method, which wasstudied by Bai et al. [Y.Q. Bai, M. El Ghami and C. Roos,
ewblock {A new efficient large-update primal-dual interior-point method based on a finite barrier,}
ewblock {SIAM J. Optim.} 13(3), 766-782 (2003)]for linear optimization to the Cartesian P*(k)-linear complementarity problem over symmetric conesvia Euclidean Jordan algebras. The symmetry of the resulting search directionsis forced by using the Nesterov-Todd scaling scheme.Moreover, we derive the iteration-bounds that match the currently bestknown iteration-bounds for large- and small-update methods, namelyO((1+2k)√￣r log r log r/ε) and O((1+2k)√￣r log r/ε), respectively,where r denotes the rank of the associated Euclidean Jordanalgebra and $ arepsilon$ the desired accuracy. |
|
| Keywords:Symmetric cone linear complementarity problem; The Cartesian P*(k)-property; Kernel function; Interior-point algorithm; Euclidean Jordan algebra |
|
