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TECHNICAL PAPERS

Optimal Design Using Chaotic Descent Method

[+] Author and Article Information
Vojin Jovanovic

Design & Manufacturing Institute, Stevens Institute of Technology, Hoboken, NJ 07030e-mail: fractal97@hotmail.com

Kazem Kazerounian

Dept. of Mech. Eng., University of Connecticut, Storrs, CT 06269e-mail: kazem@engr.uconn.edu

J. Mech. Des 122(3), 265-270 (May 01, 1998) (6 pages) doi:10.1115/1.1287498 History: Received May 01, 1998
Copyright © 2000 by ASME
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References

Jacoby, S. L. S., Kowalik, J. S., and Pizzo, J. T., 1972, Iterative Methods for Nonlinear Optimization Problems, Prentice-Hall, Englewood Cliffs, NJ.
Dennis, J. E., and Schnabel, R. B., 1996, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Society for Industrial & Applied Mathematics, Philadelphia, PA.
Wilde, D. J., 1978, Globally Optimal Design, Wiley-Interscience, New York, NY.
Jovanovic,  V. T., and Kazerounian,  K., 1998, “Using Chaos to Obtain Global Solutions in Computational Kinematics,” ASME J. Mech. Des., 120, No. 2, pp. 299–304.
Jovanovic,  V. T., and Kazerounian,  K., 1998, “On the Metrics and Coordinate-SystemInduced Sensitivity.” Int. J. Numer. Methods Eng., 42, No. 4, pp. 729–747.
Jovanovic, V., 1997, “Identifying, Utilizing and Improving Chaotic Numerical Instabilities in Computational Kinematics,” Ph.D. Thesis, The University of Connecticut, Storrs, CT.
Julia,  G., 1918, “Memoire sur l’iteration des fonctions rationelles,” J. Math. Pure Appl., 8, pp. 47–245.
Fatou,  M. P., 1919, “Sur les equations fonctionelles,” Bull. Soc. Math. Fr., 47, pp. 161–271.
Cayley,  A., 1879, “The Newton-Fourier Imaginary Problem,” Am. J. Math., 2, pp. 97.
Devaney R. L., 1989, An Introduction to Chaotic Dynamical Systems, Perseus, a division of Harper/Collins, Reading, MA.
Paradis,  M. J., and Willmert,  K. D., 1983, “Optimal Mechanism Design using the Gauss Constrained Method,” ASME J. Mech. Trans. Auto. Design, 105, pp. 187–196.

Figures

Grahic Jump Location
Basin of attraction for NR method for f(z)=z3−z
Grahic Jump Location
One-dimensional search through the variable space
Grahic Jump Location
Cutting the basins of attraction formed by CG method
Grahic Jump Location
3-D view of the objective function F(x1,x2)
Grahic Jump Location
Desired global solution

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