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The Accuracy of Interior-Point Methods Based on Kernel Functions

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  • Manuel V. C. Vieira

    (Universidade Nova de Lisboa)

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.

Suggested Citation

  • Manuel V. C. Vieira, 2012. "The Accuracy of Interior-Point Methods Based on Kernel Functions," Journal of Optimization Theory and Applications, Springer, vol. 155(2), pages 637-649, November.
    • Handle: RePEc:spr:joptap:v:155:y:2012:i:2:d:10.1007_s10957-012-0071-0
    DOI: 10.1007/s10957-012-0071-0
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    References listed on IDEAS

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    1. Peng, Jiming & Roos, Cornelis & Terlaky, Tamas, 2002. "A new class of polynomial primal-dual methods for linear and semidefinite optimization," European Journal of Operational Research, Elsevier, vol. 143(2), pages 234-256, December.
    2. Y. Q. Bai & G. Lesaja & C. Roos & G. Q. Wang & M. El Ghami, 2008. "A Class of Large-Update and Small-Update Primal-Dual Interior-Point Algorithms for Linear Optimization," Journal of Optimization Theory and Applications, Springer, vol. 138(3), pages 341-359, September.
    3. M. Reza Peyghami, 2009. "An Interior Point Approach For Semidefinite Optimization Using New Proximity Functions," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 26(03), pages 365-382.
    4. Potra, Florian A., 2002. "The Mizuno-Todd-Ye algorithm in a larger neighborhood of the central path," European Journal of Operational Research, Elsevier, vol. 143(2), pages 257-267, December.
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