On the Stability of Globally Projected Dynamical Systems

On the Stability of Globally Projected Dynamical Systems. Xia, Y. S. & Wang, J. Journal of Optimization Theory and Applications, 106(1):129–150, July, 2000.

Paper doi abstract bibtex

Two types of projected dynamical systems, whose equilibrium states solve the corresponding variational inequality problems, were proposed recently by Dupuis and Nagurney (Ref. 1) and by Friesz et al. (Ref. 2). The stability of the dynamical system developed by Dupuis and Nagurney has been studied completely (Ref. 3). This paper analyzes and proves the global asymptotic stability of the dynamical system proposed by Friesz et al. under monotone and symmetric mapping conditions. Furthermore, the dynamical system is shown to be globally exponentially stable under stronger conditions. Finally, we show that the dynamical system proposed by Friesz et al. can be applied easily to neural networks for solving a class of optimization problems.

@article{xia_stability_2000,
	title = {On the {Stability} of {Globally} {Projected} {Dynamical} {Systems}},
	volume = {106},
	issn = {0022-3239, 1573-2878},
	url = {http://link.springer.com/10.1023/A:1004611224835},
	doi = {10.1023/a:1004611224835},
	abstract = {Two types of projected dynamical systems, whose equilibrium states solve the corresponding variational inequality problems, were proposed recently by Dupuis and Nagurney (Ref. 1) and by Friesz et al. (Ref. 2). The stability of the dynamical system developed by Dupuis and Nagurney has been studied completely (Ref. 3). This paper analyzes and proves the global asymptotic stability of the dynamical system proposed by Friesz et al. under monotone and symmetric mapping conditions. Furthermore, the dynamical system is shown to be globally exponentially stable under stronger conditions. Finally, we show that the dynamical system proposed by Friesz et al. can be applied easily to neural networks for solving a class of optimization problems.},
	language = {en},
	number = {1},
	urldate = {2022-01-20},
	journal = {Journal of Optimization Theory and Applications},
	author = {Xia, Y. S. and Wang, J.},
	month = jul,
	year = {2000},
	pages = {129--150},
}

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