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۱Local Self–concordance of Barrier Functions Based on Kernel–functions Print
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اطلاعات انتشار: Iranian Journal Of Operations Research، سوم،شماره۲، ۲۰۱۲، سال
تعداد صفحات: ۲۳
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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