Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4628168 | Applied Mathematics and Computation | 2014 | 13 Pages |
Abstract
In this paper, we establish polynomial convergence of Mehrotra-type prediction corrector infeasible-interior-point method for symmetric optimization using a wide neighborhood of the central path. In order to show that the convergence of our algorithm for the commutative class of search directions, we prove the important inequality ‖x∘y‖1⩽3‖x‖F‖y‖F, where a mapping ‖·‖1 is defined by ‖x‖1=∑i=1r|λi| with the spectral decomposition x=∑i=1rλici. In particular, the complexity bound is O(r2logε-1)O(r2logε-1) for the Nesterov–Todd search direction, and O(r5/2logε-1)O(r5/2logε-1) for the xs and sx search direction. We provide some preliminary numerical results as well.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Ximei Yang, Hongwei Liu, Xiaoliang Dong,