Issue |
RAIRO-Oper. Res.
Volume 57, Number 3, May-June 2023
|
|
---|---|---|
Page(s) | 1599 - 1616 | |
DOI | https://doi.org/10.1051/ro/2023094 | |
Published online | 30 June 2023 |
An efficient multi parametric kernel function for large and small-update methods interior point algorithm for P*(κ)-horizontal linear complementarity problem
1
University of 8 May 1945 Guelma. BP 401, 24000 Guelma, Algeria . LMAH, FR-CNRS-3335, ISCN, 76600 Le Havre, France
2
Normandie University, UNIHAVRE, LMAH FR-CNRS-3335, ISCN, 76600 Le Havre, France
* Corresponding author: bouafia.mousaab@univ-guelma.dz
Received:
12
December
2022
Accepted:
12
June
2023
In this paper, we propose the first efficient multi parametric kernel function with logarithmic barrier term. A class of polynomial interior-point algorithms for P*(κ)-horizontal linear complementarity problem based on this kernel function, with parameters pi > 0 for all i ∈ 1, 2, , m, are presented. Then by using some simple analysis tools, we present a primal-dual interior point method (IPM) for P*(κ)-horizontal linear complementarity problems based on this kernel function. At the same time, we derive the complexity bounds small and large-update methods, respectively. In particular, if we take many different values of the parameters, we obtain the best known iteration bounds for the algorithms with large- and small-update methods are derived, namely, O((1 + 2κ)√n(log n)log n/ϵ) and O((1 + 2κ)√n log n/ϵ) respectively. We illustrate the performance of the proposed kernel function by some numerical results that are derived by applying our algorithm.
Mathematics Subject Classification: 60K05 / 90C05 / 90C31 / 90C51
Key words: P*(κ)-horizontal linear complementarity problem / Multi parametric kernel function / Large- and small-update methods / Interior point methods / Complexity bound
© The authors. Published by EDP Sciences, ROADEF, SMAI 2023
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