A Full-Newton Step Feasible Interior-Point Algorithm Based on a Kernel Function for <inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><msub><mrow><mi mathvariant="bold-italic">P</mi></mrow><mrow><mi mathvariant="bold">*</mi></mrow></msub><mo stretchy="false">(</mo><mi mathvariant="bold-italic">κ</mi><mo stretchy="false">)</mo></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/E32F337E-EA8F-467a-AEE8-159E7C2A08BD-M001.png"><?fx-imagestate width="19.19111061" height="10.15999985"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/E32F337E-EA8F-467a-AEE8-159E7C2A08BD-M001c.png"><?fx-imagestate width="19.19111061" height="10.15999985"?></graphic></alternatives></inline-formula>-Weighted Linear Complementarity Problem

ZHONG Jiawei; ZHANG Mingwang; GE Jing

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A Full-Newton Step Feasible Interior-Point Algorithm Based on a Kernel Function for

P_{*} (κ)

-Weighted Linear Complementarity Problem

更新时间：2026-10-21

- A Full-Newton Step Feasible Interior-Point Algorithm Based on a Kernel Function for $P_{*} (κ)$ -Weighted Linear Complementarity Problem
- Wuhan University Journal of Natural Sciences Pages: 1-10(2026)
- 作者机构：
  
  1.安徽信息工程学院数学教研室，安徽芜湖 241000
  2.三峡大学理学院，湖北宜昌 443002
- 作者简介：
  
  ZHONG Jiawei, male, Associate professor, research direction: optimization theory and algorithm. E-mail: jwzhong0718@126.com
  E-mail: zmwang@ctgu.edu.cn
- 基金信息：
- DOI：
  CLC： O221
- Received：27 September 2025，
  
  Online First：21 October 2026，
- 稿件说明：
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钟家伟,张明望,葛靖.P*(κ)-权线性互补问题基于核函数的全牛顿步可行内点算法[J].武汉大学学报自然科学英文版,

ZHONG Jiawei,ZHANG Mingwang,GE Jing.A Full-Newton Step Feasible Interior-Point Algorithm Based on a Kernel Function for P*(κ)-Weighted Linear Complementarity Problem[J].Wuhan University Journal of Natural Sciences,
钟家伟,张明望,葛靖.P*(κ)-权线性互补问题基于核函数的全牛顿步可行内点算法[J].武汉大学学报自然科学英文版, DOI：https://doi.org/10.1051/wujns/001.

ZHONG Jiawei,ZHANG Mingwang,GE Jing.A Full-Newton Step Feasible Interior-Point Algorithm Based on a Kernel Function for P*(κ)-Weighted Linear Complementarity Problem[J].Wuhan University Journal of Natural Sciences, DOI：https://doi.org/10.1051/wujns/XXXXXXXX001.

A Full-Newton Step Feasible Interior-Point Algorithm Based on a Kernel Function for

P_{*} (κ)

-Weighted Linear Complementarity Problem

PDF Download

摘要

为求解

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https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=120735241&type=

8.18444443

4.51555586

-权线性互补问题，本文提出了一种基于核函数的全牛顿步可行内点算法。算法基于带有线性增长项的核函数，进而得到一个新的牛顿搜索方向。定义了

迭代点到中心路径的邻近测度，并对算法的可行性与收敛性进行了分析。证明了算法具有目前权线性互补问题最好的多项式时间迭代复杂度。初步数值实验结果验证了算法的有效性。

Abstract

To solve

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https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=120735257&type=

7.05555630

3.95111132

-weighted linear complementarity problems

a full-Newton step feasible interior-point algorithm based on a kernel function is proposed. The kernel function has a linear growth term

which yields a new Newton search direction. We define a proximity measure for the central path and analyze the feasibility and convergence of the full-Newton step algorithm. It is shown that the proposed algorithm has the currently best-known polynomial iteration complexity. Furthermore

some preliminary numerical results are provided to demonstrate the computational performance of the algorithm.

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references

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Asadi S , Darvay Z , Lesaja G , et al A full-Newton step interior-point method for monotone weighted linear complementarity problems [J ] . Journal of Optimization Theory and Applications , 2020 , 186 ( 3 ): 864 - 878 .

Chi X N , Zhang R J , Liu S Y . A new full-Newton step feasible interior-point algorithm for linear weighted complementarity problem [J ] . Mathematica Applicata , 2021 , 34 ( 2 ): 304 - 311 (Ch) .

Kheirfam B . Complexity analysis of a full-Newton step interior-point method for monotone weighted linear complementarity problems [J ] . Journal of Optimization Theory and Applications , 2024 , 202 ( 1 ): 133 - 145 .

Zhang M W , Zhu D C , Zhong J W . A full-Newton step interior-point algorithm for the special weighted linear complementarity problem based on positive-asymptotic kernel function [J ] . Optimization and Engineering , 2024 , 25 ( 4 ): 2073 - 2091 .

Chi X N , Wang G Q , Lesaja G . Kernel-based full-Newton step feasible interior-point algorithm for <math id="M297"><msub><mrow><mi>P</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msub><mo stretchy="false">(</mo><mi>κ</mi><mo stretchy="false">)</mo></math> https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=120735744&type= https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=120735729&type= 7.05555630 3.95111132 -weighted linear complementarity problem [J ] . Journal of Optimization Theory and Applications , 2024 , 202 ( 1 ): 108 - 132 .

Geng J , Zhang M W , Zhu D C . A full-Newton step feasible interior-point algorithm for the special weighted linear complementarity problems based on a kernel function [J ] . Wuhan University Journal of Natural Sciences , 2024 , 29 ( 1 ): 29 - 37 .

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Zhang M W , Geng J , Wu S . A new infeasible interior-point algorithm with full-Newton steps for linear programming based on a kernel function [J ] . Journal of Nonlinear Functional Analysis , 2021 , Article ID 31.

Chi X N , Gan L , Gao Z R , et al A feasible interior-point method with full-Newton step for <math id="M298"><msub><mrow><mi>P</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msub><mo stretchy="false">(</mo><mi>κ</mi><mo stretchy="false">)</mo></math> https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=120735744&type= https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=120735729&type= 7.05555630 3.95111132 -weighted linear complementarity problem via the algebraically equivalent transformation [J ] . Applied Numerical Mathematics , 2026 , 220 : 144 - 166 .

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Chi X N , Zhang L , Liu S Y , et al A full-Newton step feasible interior-point algorithm for P * (κ)-linear weighted complementarity problems [J ] . Mathematica Applicata , 2023 , 36 ( 2 ): 540 - 549 (Ch) .

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A Full-Newton Step Feasible Interior-Point Algorithm Based on a Kernel Function for P*(κ)-Weighted Linear Complementarity Problem

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摘要

Abstract

关键词

Keywords

references

A Full-Newton Step Feasible Interior-Point Algorithm Based on a Kernel Function for $P_{*} (κ)$ -Weighted Linear Complementarity Problem