Chaotic descent method and fractal conjecture

Very often, when dealing with computational methods in engineering analysis , the final state depends so sensitively on the system's precise initial co nditions that the behaviour becomes unpredictable and cannot be distinguish ed from a random process. This outcome is rooted in an intricate phenomenon labelled 'chaos', which is a synonym for unpredictable events in nature. I n contrast, chaos is a deterministic feature that can be utilized for probl ems 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 comp utational instabilities in solving systems of non-linear equations and opti mization theory that resulted in development of a new method, chaotic desce nt. 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 t he systems of simultaneous non-linear equations for all the solutions. Copy right (C) 2000 John Wiley & Sons, Ltd.