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An $$\ell _{2}$$ ℓ 2 -neighborhood infeasible interior-point algorithm for linear complementarity problems

Author

Listed:
  • M. Pirhaji

    (Shahrekord University)

  • M. Zangiabadi

    (Shahrekord University)

  • H. Mansouri

    (Shahrekord University)

Abstract

In this paper, we propose an infeasible interior-point algorithm for linear complementarity problems. In every iteration, the algorithm constructs an ellipse and searches an $$\varepsilon $$ ε -approximate solution of the problem along the ellipsoidal approximation of the central path. The theoretical iteration-complexity of the algorithm is derived and the algorithm is proved to be polynomial with the complexity bound $$O\left(n\log \varepsilon ^{-1}\right)$$ O n log ε - 1 which coincides with the best known iteration bound for infeasible interior-point methods.

Suggested Citation

  • M. Pirhaji & M. Zangiabadi & H. Mansouri, 2017. "An $$\ell _{2}$$ ℓ 2 -neighborhood infeasible interior-point algorithm for linear complementarity problems," 4OR, Springer, vol. 15(2), pages 111-131, June.
    • Handle: RePEc:spr:aqjoor:v:15:y:2017:i:2:d:10.1007_s10288-016-0325-z
    DOI: 10.1007/s10288-016-0325-z
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    References listed on IDEAS

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    1. Yaguang Yang, 2013. "A Polynomial Arc-Search Interior-Point Algorithm for Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 158(3), pages 859-873, September.
    2. Yang, Yaguang, 2011. "A polynomial arc-search interior-point algorithm for convex quadratic programming," European Journal of Operational Research, Elsevier, vol. 215(1), pages 25-38, November.
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    Cited by:

    1. Sabir, Zulqurnain & Wahab, Hafiz Abdul & Umar, Muhammad & Erdoğan, Fevzi, 2019. "Stochastic numerical approach for solving second order nonlinear singular functional differential equation," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.

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