MinFinder: Locating all the local minima of a function

Abstract
A new stochastic clustering algorithm is introduced that aims to locate all the local minima of a multidimensional continuous and differentiable function inside a bounded domain. The accompanying software (MinFinder) is written in ANSI C++. However, the user may code his objective function either in C++, C or Fortran 77. We compare the performance of this new method to the performance of Multistart and Topographical Multilevel Single Linkage Clustering on a set of benchmark problems.

Title of program: MinFinder
Catalogue Id: ADWU_v1_0

Nature of problem
A multitude of problems in science and engineering are often reduced to minimizing a function of many variables. There are instances that a local optimum does not correspond to the desired physical solution and hence the search for a better solution is required. Local optimization techniques can be trapped in any local minimum. Global optimization is then the appropriate tool. For example, solving a non - linear system of equations via optimization, one may encounter many local minima that do no ...

Versions of this program held in the CPC repository in Mendeley Data
ADWU_v1_0; MinFinder; 10.1016/j.cpc.2005.10.001
ADWU_v2_0; MinFinder v2.0; 10.1016/j.cpc.2008.04.016

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)

摘要
本文提出一种全新的随机聚类算法，旨在定位有界区域内多维连续可微函数的全部局部极小值。配套软件MinFinder采用ANSI C++编写，用户可自行使用C++、C或Fortran 77语言编写目标函数。本文将该新方法的性能与多重启动法（Multistart）及地形多级单链接聚类（Topographical Multilevel Single Linkage Clustering）在一组基准测试问题上的性能进行了对比。

程序名称：MinFinder
目录编号：ADWU_v1_0

问题本质
科学与工程领域的大量问题往往可归结为多变量函数的极小化问题。部分场景中，局部最优解并不对应预期的物理解，因此需要寻找更优解。局部优化技术可能陷入任意局部极小值的陷阱，此时全局优化便是合适的解决方案。例如，通过优化方法求解非线性方程组时，可能会遇到诸多无法满足需求的局部极小值（原文此处截断为“do no ...”）。

Mendeley数据集中CPC库收录的该程序版本
ADWU_v1_0；MinFinder；10.1016/j.cpc.2005.10.001
ADWU_v2_0；MinFinder v2.0；10.1016/j.cpc.2008.04.016

本程序源自贝尔法斯特女王大学馆藏的CPC程序库（1969-2019）。