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Interior-point algorithms for symmetric cone horizontal linear complementarity problems based on a new class of algebraically equivalent transformations

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  • Darvay, Zsolt
  • Rigó, Petra Renáta

Abstract

We introduce interior-point algorithms (IPAs) for solving P_* (κ)-horizontal linear complementarity problems over Cartesian product of symmetric cones. We generalize the primal-dual IPAs proposed recently by Illés et al. [21] to P_* (κ)-horizontal linear complementarity problems over Cartesian product of symmetric cones. In the algebraic equivalent transformation (AET) technique we use a modification of the class of AET functions proposed by Illés et al. [21]. In the literature, there are only few classes of functions for determination of search directions. The class of AET functions used in this paper differs from the other classes appeared in the literature. We prove that the proposed IPAs have the same complexity bound as the best known interior-point methods for solving these types of problems.

Suggested Citation

  • Darvay, Zsolt & Rigó, Petra Renáta, 2022. "Interior-point algorithms for symmetric cone horizontal linear complementarity problems based on a new class of algebraically equivalent transformations," Corvinus Economics Working Papers (CEWP) 2022/04, Corvinus University of Budapest.
    • Handle: RePEc:cvh:coecwp:2022/04
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    File URL: https://unipub.lib.uni-corvinus.hu/7456/
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    Keywords

    Horizontal linear complementarity problem; Cartesian product of symmetric cones; new class of AET functions; interior-point algorithms;
    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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