Computational experience with globally convergent descent methods for large sparse systems of nonlinear equations

IF 1.4 3区数学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Optimization Methods & Software Pub Date : 1998-01-01 DOI:10.1080/10556789808805677

L. Luksan, J. Vlček

引用次数: 23

Abstract

This paper is devoted to globally convergent Armijo-type descent methods for solving large sparse systems of nonlinear equations. These methods include the discrete Newtcin method and a broad class of Newton-like methods based on various approximations of the Jacobian matrix. We propose a general theory of global convergence together with a robust algorithm including a special restarting strategy. This algorithm is based cfn the preconditioned smoothed CGS method for solving nonsymmetric systems of linejtr equations. After reviewing 12 particular Newton-like methods, we propose results of extensive computational experiments. These results demonstrate high efficiency of tip proposed algorithm

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大型非线性方程稀疏系统全局收敛下降法的计算经验

研究了求解大型非线性方程稀疏系统的全局收敛armijo型下降方法。这些方法包括离散牛顿法和基于雅可比矩阵的各种近似的一类类牛顿方法。我们提出了一个全局收敛的一般理论和一个包含特殊重启策略的鲁棒算法。该算法基于求解非对称线性方程组的预条件光滑CGS法。在回顾了12种特定的类牛顿方法后，我们提出了广泛的计算实验结果。实验结果表明，该算法具有较高的效率

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.