Chaotic descent method and fractal conjecture

✍ Scribed by Vojin Jovanovic

• Publisher: John Wiley and Sons
• Year: 2000
• Tongue: English
• Weight: 277 KB
• Volume: 48
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/(sici)1097-0207(20000510)48:1<137::aid-nme876>3.0.co;2-x

✦ Synopsis

Very often, when dealing with computational methods in engineering analysis, the "nal 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 "nding 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.