Corvinus
Corvinus

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

Darvay, Zsolt and Rigó, Petra Renáta (2021) New predictor-corrector interior-point algorithm for symmetric cone horizontal linear complementarity problems. Working Paper. Corvinus University of Budapest, Budapest.

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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.

Item Type:Monograph (Working Paper)
Series Name:Corvinus Economics Working Papers - CEWP
Series Number / Identification Number:2021/01
Uncontrolled Keywords:Horizontal linear complementarity problem, Cartesian product of symmetric cones, Predictor-corrector interior-point algorithm, Euclidean Jordan algebra, Algebraic equivalent transformation technique
JEL classification:A32 - Collective Volumes
A33 - Handbooks
A39 - Collective Works: Other
B00 - History of Economic Thought, Methodology, and Heterodox Approaches
Subjects:Mathematics, Econometrics
ID Code:6323
Deposited By: Ádám Hoffmann
Deposited On:04 Mar 2021 17:30
Last Modified:15 Apr 2021 15:09

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