This paper presents a comprehensive survey of methods which can be utilized to search for solutions to systems of nonlinear equations (SNEs). Our objectives with this survey are to synthesize pertinent literature in this field by presenting a thorough description and analysis of the known methods capable of finding one or many solutions to SNEs, and to assist interested readers seeking to identify solution techniques which are well suited for solving the various classes of SNEs which one may encounter in real world applications. To accomplish these objectives, we present a multi-part survey. In part one, we focused on root-finding approaches which can be used to search for solutions to a SNE without transforming it into an optimization problem. In part two, we introduce the various transformations which have been utilized to transform a SNE into an optimization problem, and we discuss optimization algorithms which can then be used to search for solutions. We emphasize the important characteristics of each method, and we discuss promising directions for future research. In part three, we will present a robust quantitative comparative analysis of methods capable of searching for solutions to SNEs.
翻译:本文对可用于寻找非线性方程系统解决办法的方法进行了全面的调查。我们通过这次调查,目的是综合这一领域的相关文献,全面描述和分析能够为非线性方程找到一种或多种解决办法的已知方法,协助感兴趣的读者寻找最适合解决在现实世界应用中可能遇到的各类非线性方程的解决方案方法。为了实现这些目标,我们提出一个多部分调查。在第一部分,我们侧重于可被用于寻找非线性方程解决方案的根基调查方法,而不会将之转化为优化问题。在第二部分,我们介绍已经用来将非线性方程转化为优化问题的各种变换,我们讨论可随后用于寻找解决方案的优化算法。我们强调每一种方法的重要特点,并讨论未来研究的有希望的方向。在第三部分,我们将对能够寻找非线性方方程解决方案的方法进行可靠的定量比较分析。