Kernel-Based Full-Newton Step Feasible Interior-Point Algorithm for $$P_{*}(\kappa )$$ P ∗ ( κ ) -Weighted Linear Complementarity Problem

Xiaoni Chi (), Guoqiang Wang () and Goran Lesaja ()
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Xiaoni Chi: Guilin University of Electronic Technology
Guoqiang Wang: Shanghai University of Engineering Science
Goran Lesaja: Georgia Southern University

Journal of Optimization Theory and Applications, 2024, vol. 202, issue 1, No 6, 108-132

Abstract: Abstract In this paper, we consider a kernel-based full-Newton step feasible interior-point method (IPM) for $$P_{*}(\kappa )$$ P ∗ ( κ ) -Weighted Linear Complementarity Problem (WLCP). The specific eligible kernel function is used to define an equivalent form of the central path, the proximity measure, and to obtain search directions. Full-Newton steps are adopted to avoid the line search at each iteration. It is shown that with appropriate choices of the parameters, and a certain condition on the starting point, the iterations always lie in the defined neighborhood of the central path. Assuming strict feasibility of $$P_{*}(\kappa )$$ P ∗ ( κ ) -WLCP, it is shown that the IPM converges to the $$\varepsilon $$ ε -approximate solution of $$P_{*}(\kappa )$$ P ∗ ( κ ) -WLCP in a polynomial number of iterations. Few numerical results are provided to indicate the computational performance of the algorithm.

Keywords: $$P_{*}(\kappa )$$ P ∗ ( κ ) -weighted linear complementarity problem; Interior-point algorithm; Full-Newton step; Polynomial complexity (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-023-02327-9

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