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New predictor-corrector interior-point algorithm for symmetric cone horizontal linear complementarity problems

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  • Darvay, Zsolt
  • Rigó, Petra Renáta

Abstract

In this paper we propose a new predictor-corrector interior-point algorithm for solving P_* (κ) horizontal linear complementarity problems defined on a Cartesian product of symmetric cones, which is not based on a usual barrier function. We generalize the predictor-corrector algorithm introduced in [13] to P_* (κ)-linear horizontal complementarity problems on a Cartesian product of symmetric cones. We apply the algebraic equivalent transformation technique proposed by Darvay [9] and we use the function φ(t)=t-√t in order to determine the new search directions. In each iteration the proposed algorithm performs one predictor and one corrector step. We prove that the predictor-corrector interior-point algorithm has the same complexity bound as the best known interior-point algorithms for solving these types of problems. Furthermore, we provide a condition related to the proximity and update parameters for which the introduced predictor-corrector algorithm is well defined.

Suggested Citation

  • Darvay, Zsolt & Rigó, Petra Renáta, 2021. "New predictor-corrector interior-point algorithm for symmetric cone horizontal linear complementarity problems," Corvinus Economics Working Papers (CEWP) 2021/01, Corvinus University of Budapest.
    • Handle: RePEc:cvh:coecwp:2021/01
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    File URL: https://unipub.lib.uni-corvinus.hu/6323/
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    More about this item

    Keywords

    Horizontal linear complementarity problem; Cartesian product of symmetric cones; Predictor-corrector interior-point algorithm; Euclidean Jordan algebra; Algebraic equivalent transformation technique;
    All these keywords.

    JEL classification:

    • A32 - General Economics and Teaching - - Multisubject Collective Works - - - Collective Volumes
    • A33 - General Economics and Teaching - - Multisubject Collective Works - - - Handbooks
    • A39 - General Economics and Teaching - - Multisubject Collective Works - - - Other
    • B00 - Schools of Economic Thought and Methodology - - General - - - History of Economic Thought, Methodology, and Heterodox Approaches

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