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Local Self-concordance of Barrier Functions Based on Kernel-functions
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Bai   , Lesaja , Mansouri , Roos , Zangiabadi |
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Abstract: (35085 Views) |
| Many efficient interior-point methods (IPMs) are based on the use of a self-concordant barrier function for the domain of the problem that has to be solved. Recently, a wide class of new barrier functions has been introduced in which the functions are not self-concordant, but despite this fact give rise to efficient IPMs. Here, we introduce the notion of locally self-concordant barrier functions and we prove that the new barrier functions are locally self-concordant. In many cases, the (local) complexity numbers of the new barrier functions along the central path are better than the complexity number of the logarithmic barrier function by a factor between 0.5 and 1. |
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| Keywords: Linear optimization, Self-dual embedding, Primal-dual interior-point method, Self-concordance, Kernel function, Polynomial complexity |
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Full-Text [PDF 852 kb]
(51075 Downloads)
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Type of Study: Original |
Received: 2013/06/21 | Accepted: 2013/06/22 | Published: 2013/06/22
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