Title
A recurrent neural network for nonlinear continuously differentiable optimization over a compact convex subset
Document Type
Article
Publication Date
11-1-2001
Abstract
In this paper, we propose a general recurrent neural-network (RNN) model for nonlinear optimization over a nonempty compact convex subset which includes the bound subset and spheroid subset as special cases. It is shown that the compact convex subset is a positive invariant and attractive set of the RNN system and that all the network trajectories starting from the compact convex subset converge to the equilibrium set of the RNN system. The above equilibrium set of the RNN system coincides with the optimum set of the minimization problem over the compact convex subset when the objective function is convex. The analysis of these qualitative properties for the RNN model is conducted by employing the properties of the projection operator of Euclidean space onto the general nonempty closed convex subset. A numerical simulation example is also given to illustrate the qualitative properties of the proposed general RNN model for solving an optimization problem over various compact convex subsets.
Publication Source (Journal or Book title)
IEEE Transactions on Neural Networks
First Page
1487
Last Page
1490
Recommended Citation
Liang, X. (2001). A recurrent neural network for nonlinear continuously differentiable optimization over a compact convex subset. IEEE Transactions on Neural Networks, 12 (6), 1487-1490. https://doi.org/10.1109/72.963784