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Abstract and Applied Analysis
Volume 2014, Article ID 710158, 11 pages
Research Article

Complexity Analysis of Primal-Dual Interior-Point Methods for Linear Optimization Based on a New Parametric Kernel Function with a Trigonometric Barrier Term

1College of Advanced Vocational Technology, Shanghai University of Engineering Science, Shanghai 200437, China
2College of Fundamental Studies, Shanghai University of Engineering Science, Shanghai 201620, China
3Nesna University College, Mathematics Section, 8700 Nesna, Norway

Received 9 February 2014; Revised 15 May 2014; Accepted 18 May 2014; Published 15 June 2014

Academic Editor: Ngai-Ching Wong

Copyright © 2014 X. Z. Cai et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We introduce a new parametric kernel function, which is a combination of the classic kernel function and a trigonometric barrier term, and present various properties of this new kernel function. A class of large- and small-update primal-dual interior-point methods for linear optimization based on this parametric kernel function is proposed. By utilizing the feature of the parametric kernel function, we derive the iteration bounds for large-update methods, , and small-update methods, . These results match the currently best known iteration bounds for large- and small-update methods based on the trigonometric kernel functions.