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A Polynomial Arc-Search Interior-Point Algorithm for Linear Programming

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  • Yaguang Yang

    (NRC)

Abstract

In this paper, ellipsoidal estimations are used to track the central path of linear programming. A higher-order interior-point algorithm is devised to search the optimizers along the ellipse. The algorithm is proved to be polynomial with the best complexity bound for all polynomial algorithms and better than the best known bound for higher-order algorithms.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:158:y:2013:i:3:d:10.1007_s10957-013-0281-0
    DOI: 10.1007/s10957-013-0281-0
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    References listed on IDEAS

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    1. Shinji Mizuno & Michael J. Todd & Yinyu Ye, 1993. "On Adaptive-Step Primal-Dual Interior-Point Algorithms for Linear Programming," Mathematics of Operations Research, INFORMS, vol. 18(4), pages 964-981, November.
    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.
    3. Renato D. C. Monteiro & Ilan Adler & Mauricio G. C. Resende, 1990. "A Polynomial-Time Primal-Dual Affine Scaling Algorithm for Linear and Convex Quadratic Programming and Its Power Series Extension," Mathematics of Operations Research, INFORMS, vol. 15(2), pages 191-214, May.
    4. Robert G. Bland & Donald Goldfarb & Michael J. Todd, 1981. "Feature Article—The Ellipsoid Method: A Survey," Operations Research, INFORMS, vol. 29(6), pages 1039-1091, December.
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    Cited by:

    1. Fabio Vitor & Todd Easton, 2022. "Projected orthogonal vectors in two-dimensional search interior point algorithms for linear programming," Computational Optimization and Applications, Springer, vol. 83(1), pages 211-246, September.
    2. 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.

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