Journal
PERIODICA MATHEMATICA HUNGARICA
Volume 73, Issue 1, Pages 27-42Publisher
SPRINGER
DOI: 10.1007/s10998-016-0119-2
Keywords
Linear optimization; Interior-point method; Full-Newton step; Search direction; Polynomial complexity
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Funding
- Romanian National Authority for Scientific Research, CNCS-UEFISCDI [PN-II-ID-PCE-2011-3-0024]
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This paper concerns a short-update primal-dual interior-point method for linear optimization based on a new search direction. We apply a vector-valued function generated by a univariate function on the nonlinear equation of the system which defines the central path. The common way to obtain the equivalent form of the central path is using the square root function. In this paper we consider a new function formed by the difference of the identity map and the square root function. We apply Newton's method in order to get the new directions. In spite of the fact that the analysis is more difficult in this case, we prove that the complexity of the algorithm is identical with the one of the best known methods for linear optimization.
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