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Chaotic descent method and fractal conjecture
Author(s) -
Jovanovic Vojin
Publication year - 2000
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(20000510)48:1<137::aid-nme876>3.0.co;2-x
Subject(s) - chaotic , maxima and minima , descent (aeronautics) , conjecture , chaos theory , fractal , mathematics , mathematical optimization , computer science , focus (optics) , algorithm , artificial intelligence , mathematical analysis , discrete mathematics , physics , engineering , aerospace engineering , optics
Very often, when dealing with computational methods in engineering analysis, the final state depends so sensitively on the system's precise initial conditions that the behaviour becomes unpredictable and cannot be distinguished from a random process. This outcome is rooted in an intricate phenomenon labelled ‘chaos’, which is a synonym for unpredictable events in nature. In contrast, chaos is a deterministic feature that can be utilized for problems of finding global solutions in both non‐linear systems of equations as well as optimization. The focus of this paper is an attempt to utilize computational instabilities in solving systems of non‐linear equations and optimization theory that resulted in development of a new method, chaotic descent . The method is based on descending to global minima via regions that are the source of computational chaos. Also, one very important conjecture is presented that in the future might lead the way towards direct solving of the systems of simultaneous non‐linear equations for all the solutions. Copyright © 2000 John Wiley & Sons, Ltd.