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A Predictor-Corrector Interior-Point Algorithm Using A Special Power Function for $P_*(\kappa)-$weighted Horizontal Linear

Chi Xiaoni et al.

Pacific Journal of Optimization2026https://doi.org/10.61208/pjo-2026-005article
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What the paper says

(Communicated by Jie Sun) In this paper, we present a predictor-corrector interior-point algorithm (PC IPA) with new search directions to solve $P_*(\kappa)-$weighted horizontal linear complementary problem (WHLCP). $P_*(\kappa)-$WHLCP includes monotone WLCP, $P_*(\kappa)-$horizontal linear complementary problem (HLCP), $P_*(\kappa)-$linear complementary problem (LCP), monotone LCP and convex quadratic programming as special cases, and could model a wide range of equilibrium problems in scientific engineering and economic management. The main idea of our PC IPA is transforming the centering equations of the central path by the algebraic equivalent transformation (AET) technique based on a power function with an arbitrary positive integer $q$. Upon analyzing the effect of different $q$ on the transformed system, we select a power function $\varphi(t) = t^{\frac{5}{2}}$ in order to get the search direction. The feasibility and global convergence of the proposed algorithm are verified under appropriate conditions. Additionally, the iteration bound of our algorithm is comparable to the best-known bounds for such available IPAs. The efficacy of the proposed algorithm is demonstrated through the presentation of numerical results.

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https://doi.org/https://doi.org/10.61208/pjo-2026-005

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@article{chi2026,
  title        = {{A Predictor-Corrector Interior-Point Algorithm Using A Special Power Function for $P_*(\kappa)-$weighted Horizontal Linear}},
  author       = {Chi Xiaoni et al.},
  journal      = {Pacific Journal of Optimization},
  year         = {2026},
  doi          = {https://doi.org/https://doi.org/10.61208/pjo-2026-005},
}

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