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The Accuracy of Interior-Point Methods Based on Kernel Functions

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Abstract

For the last decade, interior-point methods that use barrier functions induced by some real univariate kernel functions have been studied. In these interior-point methods, the algorithm stops when a solution is found such that it is close (in the barrier function sense) to a point in the central path with the desired accuracy. However, this does not directly imply that the algorithm generates a solution with prescribed accuracy. Until now, this had not been appropriately addressed. In this paper, we analyze the accuracy of the solution produced by the aforementioned algorithm.

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Acknowledgements

This work was partially supported by CMA/FCT/UNL, under Financiamento Base 2009 ISFL-1-297 from FCT/MCTES/PT.

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Authors and Affiliations

  1. CMA, Department of Mathematics, Faculty of Science and Technology, Universidade Nova de Lisboa, Quinta da Torre, 2829-516, Caparica, Portugal

    Manuel V. C. Vieira

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  1. Manuel V. C. Vieira
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Correspondence to Manuel V. C. Vieira.

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Communicated by Florian A. Potra.

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Vieira, M.V.C. The Accuracy of Interior-Point Methods Based on Kernel Functions. J Optim Theory Appl 155, 637–649 (2012). https://doi.org/10.1007/s10957-012-0071-0

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