Abstract
The projection-type neural networks \(\tau \frac{dx}{dt}=-x+P_{\Omega }(x-\Lambda (t)\partial ^{0}E(x))\) are generic and useful models for solving the constrained optimization problems min {E(x)|x ∈ Ω}. In the existing convergence/ stability analysis, the most are deduced based on the assumptions that E is uniformly or strictly convex and Ω is box-shaped. In this talk we present a generalized theory on convergence/stability of the networks. In the general setting that E is only convex and Ω is any closed bounded convex set, it is shown the global convergence/asymptotic stability of the networks in a specified sense. The presented theory sharpens and generalizes the existing results, and, consequently, underlies the applicability of the neural networks for a broader type of optimization problems.
This research was supported by the NSF project under contract No.10371097.
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Zhang, R., Xu, Z. (2005). A Generalized Global Convergence Theory of Projection-Type Neural Networks for Optimization. In: Hao, Y., et al. Computational Intelligence and Security. CIS 2005. Lecture Notes in Computer Science(), vol 3801. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11596448_115
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DOI: https://doi.org/10.1007/11596448_115
Publisher Name: Springer, Berlin, Heidelberg
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