Large-step interior-point algorithm for linear optimization based on a new wide neighbourhood

Zsolt Darvay () and Petra Renáta Takács
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Zsolt Darvay: Babeş-Bolyai University
Petra Renáta Takács: Babeş-Bolyai University

Central European Journal of Operations Research, 2018, vol. 26, issue 3, No 3, 563 pages

Abstract: Abstract The interior-point algorithms can be classified in multiple ways. One of these takes into consideration the length of the step. In this way, we can speak about large-step and short-step methods, that work in different neighbourhoods of the central path. The large-step algorithms work in a wide neighbourhood, while the short-step ones determine the new iterates that are in a smaller neighbourhood. In spite of the fact that the large-step algorithms are more efficient in practice, the theoretical complexity of the short-step ones is generally better. Ai and Zhang introduced a large-step interior-point method for linear complementarity problems using a wide neighbourhood of the central path, which has the same complexity as the best short-step methods. We present a new wide neighbourhood of the central path. We prove that the obtained large-step primal–dual interior-point method for linear programming has the same complexity as the best short-step algorithms.

Keywords: Linear programming; Large-step algorithm; Wide neighbourhood; Polynomial complexity (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10100-018-0524-0

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