Research On Optimization Problems And Associative Memories Via Delayed Neural Networks

Optimization problems and associative memories have attracted much attention due to its wide ap-plication in engineering and scientific research,and they have become the most popular research fields by using neural networks.With the enlargement of the scale,traditional methods can't meet the demands of increasing development of social economy.Because artificial neural networks have the advantages of massively parallel processing,fast convergence rate,hardware implementation and control,they are used for solving optimization problem and associative memories,which have attracted the attention of domestic and foreign scholars and become a hot research field.The main aim is to discuss some delayed neural networks for solving optimization and associative memories.By the(partial)functional differ-ential theory,stability analysis,the Lyapunov method,differential inequality technique and MATLAB simulations,we devote to study on neural network methods for the dynamic analysis and neural networks for solving optimization and synthesizing associative memories and have obtained some meaningful re-sults.1.A new delayed projection neural network is presented for solving general convex quadratic pro-gramming problems subject to linear constraints.Based on the theory of functional differential equation,the existence and uniqueness of the continuous solution are proved.By utilizing differential inequality technique,the criterion of global exponential stability is given for the delayed projection neural network.Compared with the existing results,the proposed neural network has an one-layer architecture and fewer neurons,and complexity and difficulty of computation can be reduced.The proper time delay can ac-celerate the convergence rate of neural network,and the regulation of multi-parameter is beneficial to the stability of neural network.2.A nonsmooth projection neural network with discrete and distributed delays is presented for solving linear variational inequality problems.By employing matrix measure,differential inequality technique and the theory of functional differential equation,we obtained some novel sufficient conditions ensuring globally exponential stability.The lower conservatism of the stability condition expands the scope of application of time-delayed neural network,which improved the results of related literatures.Finally,some simulation results with applications to finance and image fusion are given to demonstrate the effective performance of the neural network with a layer structure.3.A new delayed projection neural network with reaction-diffusion terms is considered for solving non-monotone linear variational inequality problems.The proposed neural network can be implemented by a circuit with a one-layer structure.By employing differential inequality technique and constructing a new Lyapunov-Krasovskii function,some novel sufficient conditions are obtained ensuring globally exponential stability.The research shows that the stability conditions are dependent on diffusions and monotonicity assumption is unnecessary.The appropriate delay can change the stability of the neural network and it is beneficial to solve more general non-monotone linear inequality problems.The intro-duction of diffusion meets the condition of the stability,where Mis a positive definite matrix.Namely,the reaction-diffusion neural network can solve a class of non-monotone variational problem.A larger?yields a better convergence rate.4.An extended continuous bidirectional auto-associative memory network is considered to behave as associative memories.Based on the retrieval probe as external input and the mathematical analysis method,the dynamic of each state component of the associative network can be tracked.By using the functional differential theory and Lyapunov method,the globally exponentially stable criteria are de-rived for the networks.Besides,to recall more prototype patterns simultaneously,we present a new ring recurrent network behave as associative memories.The proposed networks with high storage capacity are robust in terms of design parameter selection,which improve the results of related literature.The approach,by generating networks where the input datas are fed via external inputs rather than initial conditions,avoids the spurious equilibrium and enables multiple prototype patterns to be retrieved si-multaneously.Compared with the existing results,we can design auto-associative memory for retrieving two or three patterns at the same time.This brings new insight into associative memories of multiple patterns.5.A unified method is designed for multi-valued auto-associative and hetero-associative memories based on a continuous neural network(CNN).By using the mathematical analysis method,the dynamic of each state component of the associative network can be tracked.Combined with functional differen-tial equation and matrix analysis theory,some globally exponentially stable criteria are obtained,which provide less conservative.By utilizing the techniques of permutation matrix and generalized inverse,a unified way is presented for synthesizing both auto-associative memories and hetero-associative mem-ories.Results show that the selection of network parameters is dependent on a set of inequalities rather than the learning procedure.The lower conservative stable criteria expand the scope of the parameter.The piecewise linear nondecreasing activation function is proposed to ensure multi-valued associative patterns to be retrieved accurately.The proposed CNN is robust in terms of design parameter selec-tion and achieves(2r)~nmemory capacity.Also research results have been successfully applied to the multi-value associative memories of characters and images.