Visualization and Genetic Algorithms in Minimax Theory for Nonlinear Functionals

Springer Science and Business Media LLC - Tập 18 - Trang 49-68 - 2003
Xiyu Liu1, John Frazer2, Ming Xi Tang2
1The Design Technology Research Center, School of Design, The Hong Kong Polytechnic University, Kowloon, Hong Kong, SAR. School of Information and Management, Shandong Normal University, Jinan, Shandong, People's Republic of China
2School of Design, The Hong Kong Polytechnic University, Kowloon, Hong Kong, SAR

Tóm tắt

In this paper, evolution and visualization of the existence of saddle points of nonlinear functionals or multi-variable functions in finite dimensional spaces are presented. New algorithms are developed based on the mountain pass lemma and link thery in nonlinear analysis. Further more, a simple comparison of the steepest descent algorithm and the genetic algorithm is given. The process of the saddle point finding is visualised in an inteactive graphical interface.

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Tài liệu tham khảo

Rhyne, T.-M. (2000). Scientific visualization in the next millennium. IEEE. Comput. Graph. 20-21.--

Kasik, D. J. (2000). Viewing the future of CAD. IEEE. Comput. Graph. 34-35.--

Qin, H., and Terzopoulos, D. (1996). D-NURBS: A physics-based framework for geometric design. IEEE T. Vis. Comput. Graph. 2, 85-96.--

Gross, M. H., and Koch, R. (1995). Visualization of multidimensional shape and texture features in laser range data using complex valued Gabor wavelets. IEEE T. Vis. Comput. Graph. 1, 44-59.--

Chang, K. C. (1996). Critical Point Theory and Applications, Shanghai Science and Technological Press, Shanghai.--

Cappozzi. (1982). On subquadratic not autonomous Hamiltonian system. Lecture Notes in Math. 1017, Equadiff 82.--

Davis, L. (1991). Handbook of Genetic Algorithms, Van Nostrand Reinhold, New York, NY.--

Gen, Mitsuo, and Cheng, R. W. (1997). Genetic Algorithms and Engineering Design, Wiley Intersciences.--

Goldberg, D. E. (1989). Genetic Algorithms in Search, Optimization and Machine Learning, Addison–Wesley.--

Frazer, J. H. (1995). An Evolutionary Architecture, Architectural Association, London.--

Sun, J. (2001) Application of Genetic Algorithms to Generative Product Design Support Systems, Ph.D. thesis, The Hong Kong Polytechnic University.--

Robinowitz, P. H. (1971). Some global results for nonlinear eigenvalue problems. J. Funct. Anal. 7, 487-513.----

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Springer Science and Business Media LLC

Tập 18

49-68

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