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A Full-Newton Step Infeasible Interior-Point Algorithm for Linear Programming Based on a Kernel Function

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Abstract

This paper proposes an infeasible interior-point algorithm with full-Newton step for linear programming, which is an extension of the work of Roos (SIAM J. Optim. 16(4):1110–1136, 2006). The main iteration of the algorithm consists of a feasibility step and several centrality steps. We introduce a kernel function in the algorithm to induce the feasibility step. For parameter p∈[0,1], the polynomial complexity can be proved and the result coincides with the best result for infeasible interior-point methods, that is, O(nlog n/ε).

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Authors and Affiliations

  1. College of Science, Hohai University, Nanjing, 210098, China

    Zhongyi Liu

  2. School of Mathematics and Computer Science, Nanjing Normal University, Nanjing, 210097, China

    Wenyu Sun

  3. Department of Modern Mechanics, University of Science and Technology of China, Anhui, 230027, China

    Fangbao Tian

Authors
  1. Zhongyi Liu
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  2. Wenyu Sun
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  3. Fangbao Tian
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Corresponding author

Correspondence to Zhongyi Liu.

Additional information

This work was supported in part by the National Natural Science Foundation of China under Grant No. 10871098.

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Liu, Z., Sun, W. & Tian, F. A Full-Newton Step Infeasible Interior-Point Algorithm for Linear Programming Based on a Kernel Function. Appl Math Optim 60, 237–251 (2009). https://doi.org/10.1007/s00245-009-9069-x

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  • DOI: https://doi.org/10.1007/s00245-009-9069-x

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