多面体锥体上 R0 型广义 LCP 的全局误差边界估计算法及其应用

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2024-09-21 DOI:10.1016/j.cam.2024.116288

Hongchun Sun , Yiju Wang , Jiakang Du

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引用次数: 0

摘要

对于多面体圆锥上的广义线性互补问题（GLCP），通过对 R0 矩阵进行表征，我们推导出了 GLCP 自然残差函数水平集有界性的必要条件和充分条件，并在此基础上建立了 R0 型 GLCP 的全局误差约束。与现有结果相比，取消了对 GLCP 的要求，如解的非退化性和底层矩阵的全列秩。作为所得结果的应用，我们展示了 GLCP 矩阵分割算法的全局线性收敛性。我们还提供了一些数值实验来证明所获结果的有效性。

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Global error bound estimates algorithm for an R0-type generalized LCP over polyhedral cone and its applications

For the generalized linear complementarity problem over a polyhedral cone (GLCP), by making a characterization of

R_{0}

-matrix, we derive a necessary and sufficient condition for the boundedness of the level set of the natural residual function of the GLCP, and based on this, we establish a global error bound for the

R_{0} -

type GLCP. Compared with the existing results, the requirements imposed on the GLCP such as the non-degenerateness of the solution and the full-column rank of the underlying matrix are removed. As an application of the obtained results, we show the global linear convergence of the matrix splitting algorithm for the GLCP. Some numerical experiments are provided to show the validity of the obtained results.

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来源期刊

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.