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

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Listed:
  • X. Z. Cai
  • G. Q. Wang
  • M. El Ghami
  • Y. J. Yue

Abstract

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, O(n2/3log⁡(n/ε)), and small‐update methods, O(nlog⁡(n/ε)). These results match the currently best known iteration bounds for large‐ and small‐update methods based on the trigonometric kernel functions.

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Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:710158
DOI: 10.1155/2014/710158
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