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

•A new predictor-corrector interior-point algorithm for P*(κ)-LCPs is introduced.•A new type of algebraic equivalent transformation technique is used.•Polynomial complexity in the size of the problem and in the handicap of the matrix.•Numerical results show the efficiency of the introduced interior-...

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Bibliographic Details
Published in:	European journal of operational research Vol. 298; no. 1; pp. 25 - 35
Main Authors:	Darvay, Zsolt, Illés, Tibor, Rigó, Petra Renáta
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 01.04.2022
Subjects:	[formula omitted]-linear complementarity problem Interior-point methods Polynomial iteration complexity Predictor-corrector algorithm P(κ)-linear complementarity problem Interior-point methods Polynomial iteration complexity Predictor-corrector algorithm
ISSN:	0377-2217, 1872-6860
Online Access:	Get full text
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Summary:	•A new predictor-corrector interior-point algorithm for P(κ)-LCPs is introduced.•A new type of algebraic equivalent transformation technique is used.•Polynomial complexity in the size of the problem and in the handicap of the matrix.•Numerical results show the efficiency of the introduced interior-point algorithm. 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 and Takács (2018) for linear optimization. The search direction discussed in this paper can be derived from positive-asymptotic kernel function using the function φ(t)=t2 in the new type of AET. We prove that the IPA has O((1+4κ)nlog3nμ04ϵ) 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.
ISSN:	0377-2217 1872-6860
DOI:	10.1016/j.ejor.2021.08.039