Visualization and Genetic Algorithms in Minimax Theory for Nonlinear Functionals

Authors:
Xiyu Liu;John Frazer;Ming Xi Tang
Affiliations:
The 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, Sha ...;School of Design, The Hong Kong Polytechnic University, Kowloon, Hong Kong, SAR. sdfrazer@polyu.edu.hk;School of Design, The Hong Kong Polytechnic University, Kowloon, Hong Kong, SAR. sdtang@polyu.edu.hk
Venue:
Journal of Scientific Computing
Year:
2003

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Visualization

Abstract

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.