Application of the interval analysis for the search of the global extremum of functions

Аuthors

Panovskiy V. N.

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

e-mail: panovskiy.v@gmail.com

Abstract

Object of research in the given work are the developed methods of search of a global extremum of the functions, based on the theory of the interval analysis: method of a dichotomy of a direct image, method imaginary values cutoff and method of colonies.The objectives of the given work were detecting of possibility of effective application of the interval analysis as a base component of methods of global optimization, the formulation and the decision of the problems interfering its effective application, working out of algorithms, scheduling of improvement of the developed algorithms.The result of the given work is formation algorithmic and program software of all three methods which efficiency is shown on an example of search of a global extremum of the several typical functions with isolines of different difficulty level.

Keywords:

globalextremum; intervalanalysis; wrappingeffect; inclusionfunction; optimization

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