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In this paper, a variant of Mehrotra-type predictor–corrector algorithm is proposed for \(P_{*}(\kappa )\) linear complementarity problems. In this algorithm, a safeguard step is used to avoid small step sizes and a new corrector direction is adopted. The algorithm has polynomial iteration complexity and the iteration bound is \(O ((14\kappa +11)\sqrt{(1+4 \kappa )(1+2\kappa )}~n\log \frac{(x^{0})^{T}s^{0}}{\varepsilon } )\) . Some numerical results are reported as well.
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