The vertical linear complementarity problem associated with P o-matrices

IF 1.4 3区数学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Optimization Methods & Software Pub Date : 1999-01-01 DOI:10.1080/10556789908805739

Aniekan Ebiefung

引用次数: 3

Abstract

We show that the vertical linear complementarity problem can be solved, under certain conditions, by solving a perturbed problem when the associated matrix is a vertical block P o-matrix. The main conditions do not depend on nondegeneracy of the problem or on the matrix class to which the P o matrix may also belong. In the special case of the K o-matrices, the least element solution of the perturbed problem converges to the least element solution of the original problem.

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与P - o矩阵相关的垂直线性互补问题

我们证明了在一定条件下，当相关矩阵为垂直块P - o矩阵时，可以通过求解摄动问题来求解垂直线性互补问题。主要条件不依赖于问题的非简并性，也不依赖于P o矩阵所属的矩阵类。在K -矩阵的特殊情况下，扰动问题的最小元解收敛于原问题的最小元解。

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

Optimization Methods & Software 工程技术-计算机：软件工程

CiteScore

4.50

自引率

0.00%

发文量

审稿时长

7 months

期刊介绍： Optimization Methods and Software publishes refereed papers on the latest developments in the theory and realization of optimization methods, with particular emphasis on the interface between software development and algorithm design. Topics include: Theory, implementation and performance evaluation of algorithms and computer codes for linear, nonlinear, discrete, stochastic optimization and optimal control. This includes in particular conic, semi-definite, mixed integer, network, non-smooth, multi-objective and global optimization by deterministic or nondeterministic algorithms. Algorithms and software for complementarity, variational inequalities and equilibrium problems, and also for solving inverse problems, systems of nonlinear equations and the numerical study of parameter dependent operators. Various aspects of efficient and user-friendly implementations: e.g. automatic differentiation, massively parallel optimization, distributed computing, on-line algorithms, error sensitivity and validity analysis, problem scaling, stopping criteria and symbolic numeric interfaces. Theoretical studies with clear potential for applications and successful applications of specially adapted optimization methods and software to fields like engineering, machine learning, data mining, economics, finance, biology, or medicine. These submissions should not consist solely of the straightforward use of standard optimization techniques.