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Manuscript Title: MinFinder: Locating all the local minima of a function
Authors: Ioannis G. Tsoulos, Isaac E. Lagaris
Program title: MinFinder
Catalogue identifier: ADWU_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 174(2006)166
Programming language: GNU-C++, GNU-C, GNU Fortran - 77.
Computer: The tool is designed to be portable in all systems running the GNU C++ compiler.
Operating system: The tool is designed to be portable in all systems running the GNU C++ compiler.
RAM: 200KB
Word size: 32
Keywords: Global optimization, stochastic methods, Monte Carlo, clustering, region of attraction.
PACS: 02.60.-x, 02.60.Pn, 07.05.Kf, 02.70.Lq.
Classification: 4.9.

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 not correspond to solutions, i.e. they are far from zero.

Solution method:
Using a uniform pdf, points are sampled from the rectangular search domain. A clustering technique, based on a typical distance and a gradient criterion, is used to decide from which points a local search should be started. The employed local procedure is a BFGS version due to Powell. Further searching is terminated when all the local minima inside the search domain are thought to be found. This is accomplished via the double-box rule.

Running time:
Depending on the objective function.