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Interior point method on semi-definite linear complementarity problems using the Nesterov–Todd (NT) search direction: polynomial complexity and local convergence

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  • Chee-Khian Sim

    (University of Portsmouth)

Abstract

We consider in this paper an infeasible predictor–corrector primal–dual path following interior point algorithm using the Nesterov–Todd search direction to solve semi-definite linear complementarity problems. Global convergence and polynomial iteration complexity of the algorithm are established. Two sufficient conditions are also given for superlinear convergence of iterates generated by the algorithm. Preliminary numerical results are finally provided when the algorithm is used to solve semi-definite linear complementarity problems.

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  • 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.
    • Handle: RePEc:spr:coopap:v:74:y:2019:i:2:d:10.1007_s10589-019-00110-z
    DOI: 10.1007/s10589-019-00110-z
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    References listed on IDEAS

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    6. Chee-Khian Sim, 2011. "Asymptotic Behavior of Underlying NT Paths in Interior Point Methods for Monotone Semidefinite Linear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 148(1), pages 79-106, January.
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