非线性等式和不等式系统的填充函数方法

IF 2.5 3区数学 Q1 MATHEMATICS, APPLIED

Computational & Applied Mathematics Pub Date : 2012-08-28 DOI:10.1590/S1807-03022012000200010

Z. Wan, Liuyang Yuan, Jiawei Chen

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引用次数: 16

摘要

本文提出了一种求解非线性等式和不等式系统的填充函数法。首先，将原问题转化为等效约束全局优化问题。然后，根据重构优化问题的特点，构造一个新的单参数填充函数。对填充函数的一些性质进行了研究和讨论。最后，给出了一种基于所提出的填充函数求解非线性等式和不等式系统的算法。在填充函数算法的每次迭代中，目标函数值可以减少一半。文中给出了该算法在若干测试问题上的实现，并给出了数值结果。数学学科分类:65K05、90C30。

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A filled function method for nonlinear systems of equalities and inequalities

In this paper a filled function method is suggested for solving nonlinear systems of equalities and inequalities. Firstly, the original problem is reformulated into an equivalent constrained global optimization problem. Subsequently, a new filled function with one parameter is constructed based on the special characteristics of the reformulated optimization problem. Some properties of the filled function are studied and discussed. Finally, an algorithm based on the proposed filled function for solving nonlinear systems of equalities and inequalities is presented. The objective function value can be reduced by half in each iteration of our filled function algorithm. The implementation of the algorithm on several test problems is reported with numerical results. Mathematical subject classification: 65K05, 90C30.

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来源期刊

Computational & Applied Mathematics Mathematics-Computational Mathematics

CiteScore

4.50

自引率

11.50%

发文量

352

审稿时长

>12 weeks

期刊介绍： Computational & Applied Mathematics began to be published in 1981. This journal was conceived as the main scientific publication of SBMAC (Brazilian Society of Computational and Applied Mathematics). The objective of the journal is the publication of original research in Applied and Computational Mathematics, with interfaces in Physics, Engineering, Chemistry, Biology, Operations Research, Statistics, Social Sciences and Economy. The journal has the usual quality standards of scientific international journals and we aim high level of contributions in terms of originality, depth and relevance.