A Recurrent Neural Network for Nonlinear Continuously Differentiable Optimization Over a Compact Convex Subset  

Oleh:

Liang, Xue-Bin

Jenis: Article from Journal - ilmiah internasional
Dalam koleksi: IEEE Transactions on Neural Networks vol. 12 no. 6 (2001), page 1487-1490.
Topik: functions convex; neural network; non linear; compact; convex subset

Ketersediaan

Perpustakaan Pusat (Semanggi) Nomor Panggil: II36.6 Non-tandon: 1 (dapat dipinjam: 0) Tandon: tidak ada

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Isi artikel

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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