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Title: Complexity Analysis of Primal-Dual Interior-Point Methods for Linear Optimization Based on a New Parametric Kernel Function with a Trigonometric Barrier Term.
Authors: Cai, X. Z.; Wang, G. Q.; El Ghami, M.; Yue, Y. J.
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(√n log(n/ε)). These results match the currently best known iteration bounds for large- and small-update methods based on the trigonometric kernel functions.
Subjects: COMPUTATIONAL complexity; MATHEMATICAL optimization; KERNEL functions; TRIGONOMETRIC functions; GEOMETRIC function theory; COMPLEX variables
Publication: Abstract & Applied Analysis, 2014, p1
ISSN: 1085-3375
Publication type: Academic Journal
DOI: 10.1155/2014/710158

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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.