A neural network model for non-smooth optimization over a compact convex subset

Authors:
Guocheng Li;Shiji Song;Cheng Wu;Zifang Du
Affiliations:
Department of Automation, Tsinghua University, Beijing, China;Department of Automation, Tsinghua University, Beijing, China;Department of Automation, Tsinghua University, Beijing, China;School of Statistics, Renmin University, China
Venue:
ISNN'06 Proceedings of the Third international conference on Advances in Neural Networks - Volume Part I
Year:
2006

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Abstract

A neural network model is introduced which is aimed to solve non-smooth optimization problem on a nonempty compact convex subset of Rn. By using the subgradient, this neural network model is shown to obey a gradient system of differential inclusion. It is proved that the compact convex subset is a positive invariant and is a attractive to the neural network system, and that all the network trajectories starting from the inside of the compact convex subset converge to the set of equilibrium points of the neural network. The above every equilibrium point of the neural network is an optimal solution of the primal problem. A numerical simulation example is also given to illustrate the qualitative properties of the proposed neural network model.