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New predictor-corrector interior-point algorithm with AET function having inflection point

Author

Listed:
  • Illés, Tibor
  • Rigó, Petra Renáta
  • Török, Roland

Abstract

In this paper we introduce a new predictor-corrector interior-point algorithm for solving P_* (κ)-linear complementarity problems. For the determination of search directions we use the algebraically equivalent transformation (AET) technique. In this method we apply the function φ(t)=t^2-t+√t which has inflection point. It is interesting that the kernel corresponding to this AET function is neither self-regular, nor eligible. We present the complexity analysis of the proposed interior-point algorithm and we show that it's iteration bound matches the best known iteration bound for this type of PC IPAs given in the literature. It should be mentioned that usually the iteration bound is given for a fixed update and proximity parameter. In this paper we provide a set of parameters for which the PC IPA is well defined. Moreover, we also show the efficiency of the algorithm by providing numerical results.

Suggested Citation

  • Illés, Tibor & Rigó, Petra Renáta & Török, Roland, 2022. "New predictor-corrector interior-point algorithm with AET function having inflection point," Corvinus Economics Working Papers (CEWP) 2022/05, Corvinus University of Budapest.
    • Handle: RePEc:cvh:coecwp:2022/05
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    File URL: https://unipub.lib.uni-corvinus.hu/7724/
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    More about this item

    Keywords

    Predictor-corrector; Linear complementarity problems; Interior-point algorithm; Complexity analysis;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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