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Showing 2 results for Mansouri
Mansouri, Siyavash, Zangiabadi,
Volume 3, Issue 1 (4-2012)
Abstract
We present a new algorithm obtained by changing the search directions in the algorithm given in [8]. This algorithm is based on a new technique for finding the search direction and the strategy of the central path. At each iteration, we use only the full Nesterov-Todd (NT)step. Moreover, we obtain the currently best known iteration bound for the infeasible interior-point algorithms with full NT steps, namely O(nlogn/e) , which is as good as the linear analogue.
Bai, Lesaja, Mansouri, Roos, Zangiabadi,
Volume 3, Issue 2 (9-2012)
Abstract
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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