A recurrent neural network for nonlinear continuouslydifferentiable optimization over a compact convex subset
Xue-Bin Liang
Neural Networks, IEEE Transactions on
Volume 12, Issue 6, Nov 2001 Page(s):1487 - 1490
Digital Object Identifier 10.1109/72.963784
Summary: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
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