A new nonlinear ABS-type algorithm and its efficiency analysis ∗

IF 1.4 3区数学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Optimization Methods & Software Pub Date : 1998-01-01 DOI:10.1080/10556789808805702

N. Deng, Z. Chen

引用次数: 2

Abstract

As a continuation work following [4] and [5], a new ABS-type algorithm for a nonlinear system of equations is proposed. A major iteration of this algorithm requires n component evaluations and only one gradient evaluation. We prove that the algorithm is superlinearly convergent with R-order at least τ n , where τ n is the unique positive root of τn −τn−1 −1=0. It is shown that the new algorithm is usually more efficient than the methods of Newton, Brown and Brent, and the ABS-type algorithms in [1], [4] and [5], in the sense of some standard efficiency measure.

查看原文本刊更多论文

一种新的非线性abs型算法及其效率分析

作为继[4]和[5]之后的延续工作，提出了一种新的求解非线性方程组的abs型算法。该算法的一次主要迭代需要n个分量评估和一次梯度评估。我们证明了该算法在r阶至少τn下是超线性收敛的，其中τn是τn−τn−1−1=0的唯一正根。结果表明，在某种标准效率度量的意义上，新算法通常比Newton、Brown和Brent方法以及[1]、[4]和[5]中的abs型算法效率更高。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.