A feasible interior-point method with full-Newton step for P*(κ)-weighted linear complementarity problem via the algebraically equivalent transformation

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2026-02-01 Epub Date: 2025-10-10 DOI:10.1016/j.apnum.2025.10.003

Xiaoni Chi , Lin Gan , Zhuoran Gao , Jein-Shan Chen

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引用次数: 0

Abstract

This paper investigates feasible interior-point method (IPM) with full-Newton step for

P_{*} (κ)

-weighted linear complementarity problem (WLCP). In particular, by applying the algebraically equivalent transformation (AET) for linear optimization, we obtain the new search directions by solving the perturbed Newton system. The AET of the Newton system is based on the kernel function

φ (t) = t - \sqrt{t}

, which is used for solving WLCP for the first time. At each iteration, our algorithm takes only full-Newton steps. Therefore, no line-searches are needed to update the iterates. We show the strict feasibility of the full-Newton step and the polynomial iteration complexity of our algorithm under suitable assumptions. Some numerical experiments demonstrate the effectiveness of the proposed algorithm.

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基于代数等价变换的P*(κ)-加权线性互补问题可行的全牛顿步内点法

研究了P*(κ)加权线性互补问题的全牛顿步可行内点法。特别地，我们利用代数等价变换（AET）进行线性优化，通过求解扰动牛顿系统得到新的搜索方向。牛顿系统的AET基于核函数φ(t)=t−t，首次用于求解WLCP。在每次迭代中，我们的算法只需要一整牛顿步。因此，更新迭代时不需要行搜索。在适当的假设条件下，证明了算法的多项式迭代复杂度和全牛顿步的严格可行性。数值实验证明了该算法的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.