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A Mehrotra-type predictor-corrector algorithm with polynomiality andQ-subquadratic convergence

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Abstract

Mehrotra's predictor-corrector algorithm [3] is currently considered to be one of the most practically efficient interior-point methods for linear programming. Recently, Zhang and Zhang [18] studied the global convergence properties of the Mehrotra-type predictor-corrector approach and established polynomial complexity bounds for two interior-point algorithms that use the Mehrotra predictor-corrector approach. In this paper, we study the asymptotic convergence rate for the Mehrotra-type predictor-corrector interior-point algorithms. In particular, we construct an infeasible-interior-point algorithm based on the second algorithm proposed in [18] and show that while retaining a complexity bound ofO(n 1.5 t)-iterations, under certain conditions the algorithm also possesses aQ-subquadratic convergence, i.e., a convergence ofQ-order 2 with an unboundedQ-factor.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Maryland Baltimore County, 21228-5398, Baltimore, MD, USA

    Detong Zhang & Yin Zhang

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  1. Detong Zhang
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  2. Yin Zhang
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Research supported in part by NSF DMS-9102761 and DOE DE-FG02-93ER25171.

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Zhang, D., Zhang, Y. A Mehrotra-type predictor-corrector algorithm with polynomiality andQ-subquadratic convergence. Ann Oper Res 62, 131–150 (1996). https://doi.org/10.1007/BF02206814

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