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A primal-dual interior-point method based on various selections of displacement step for symmetric optimization

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  • Baha Alzalg

    (The University of Jordan
    Rochester Institute of Technology)

Abstract

In this paper, we develop a primal-dual central trajectory interior-point algorithm for symmetric programming problems and establish its complexity analysis. The main contribution of the paper is that it uniquely equips the central trajectory algorithm with various selections of the displacement step while solving symmetric programming. To show the efficiency of the proposed algorithm, these selections of calculating the displacement step are compared in numerical examples for second-order cone programming, which is a special case of symmetric programming.

Suggested Citation

  • Baha Alzalg, 2019. "A primal-dual interior-point method based on various selections of displacement step for symmetric optimization," Computational Optimization and Applications, Springer, vol. 72(2), pages 363-390, March.
    • Handle: RePEc:spr:coopap:v:72:y:2019:i:2:d:10.1007_s10589-018-0045-8
    DOI: 10.1007/s10589-018-0045-8
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    References listed on IDEAS

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    1. Alzalg, Baha, 2015. "Volumetric barrier decomposition algorithms for stochastic quadratic second-order cone programming," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 494-508.
    2. Baha Alzalg, 2014. "Homogeneous Self-dual Algorithms for Stochastic Second-Order Cone Programming," Journal of Optimization Theory and Applications, Springer, vol. 163(1), pages 148-164, October.
    3. Roger Behling & Clovis Gonzaga & Gabriel Haeser, 2014. "Primal-Dual Relationship Between Levenberg–Marquardt and Central Trajectories for Linearly Constrained Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 162(3), pages 705-717, September.
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    Cited by:

    1. Chee-Khian Sim, 2019. "Interior point method on semi-definite linear complementarity problems using the Nesterov–Todd (NT) search direction: polynomial complexity and local convergence," Computational Optimization and Applications, Springer, vol. 74(2), pages 583-621, November.

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    1. Baha Alzalg & Khaled Badarneh & Ayat Ababneh, 2019. "An Infeasible Interior-Point Algorithm for Stochastic Second-Order Cone Optimization," Journal of Optimization Theory and Applications, Springer, vol. 181(1), pages 324-346, April.
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