Complexity Analysis of Primal-Dual Interior-Point Methods for Linear Optimization Based on a New Parametric Kernel Function with a Trigonometric Barrier Term
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 th...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/710158 |
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| Summary: | 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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| ISSN: | 1085-3375 1687-0409 |