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

Zsolt Darvay and Petra Renáta Rigó

Corvinus Economics Working Papers (CEWP) from Corvinus University of Budapest

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.

Keywords: Horizontal linear complementarity problem; Cartesian product of symmetric cones; Predictor-corrector interior-point algorithm; Euclidean Jordan algebra; Algebraic equivalent transformation technique (search for similar items in EconPapers)
JEL-codes: A32 A33 A39 B00 (search for similar items in EconPapers)
Date: 2021-03-01
New Economics Papers: this item is included in nep-cmp and nep-ore
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Persistent link: https://EconPapers.repec.org/RePEc:cvh:coecwp:2021/01

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