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Predictor-corrector interior-point algorithm for sufficient linear complementarity problems based on a new type of algebraic equivalent transformation technique

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  • Darvay, Zsolt
  • Illés, Tibor
  • Rigó, Petra Renáta

Abstract

We propose a new predictor-corrector (PC) interior-point algorithm (IPA) for solving linear complementarity problem (LCP) with P_* (κ)-matrices. The introduced IPA uses a new type of algebraic equivalent transformation (AET) on the centering equations of the system defining the central path. The new technique was introduced by Darvay et al. [21] for linear optimization. The search direction discussed in this paper can be derived from positive-asymptotic kernel function using the function φ(t)=t^2 in the new type of AET. We prove that the IPA has O(1+4κ)√n log⁡〖(3nμ^0)/ε〗 iteration complexity, where κ is an upper bound of the handicap of the input matrix. To the best of our knowledge, this is the first PC IPA for P_* (κ)-LCPs which is based on this search direction.

Suggested Citation

  • Darvay, Zsolt & Illés, Tibor & Rigó, Petra Renáta, 2020. "Predictor-corrector interior-point algorithm for sufficient linear complementarity problems based on a new type of algebraic equivalent transformation technique," Corvinus Economics Working Papers (CEWP) 2020/03, Corvinus University of Budapest.
    • Handle: RePEc:cvh:coecwp:2020/03
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    File URL: https://unipub.lib.uni-corvinus.hu/5908/
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    Keywords

    Predictor-corrector interior-point algorithm; P_* (κ)-linear complementarity problem; new search direction; polynomial iteration complexity;
    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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