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This paper develops a neural network for solving the general nonsmooth convex optimization problems. The proposed neural network is modeled by a differential inclusion. Compared with the existing neural networks for solving nonsmooth convex optimization problems, this neural network has a wider domain for implementation. Under a suitable assumption on the constraint set, it is proved that for a given nonsmooth convex optimization problem and sufficiently large penalty parameters, any trajectory of the neural network can reach the feasible region in finite time and stays there thereafter. Moreover, we can prove that the trajectory of the neural network constructed by a differential inclusion and with arbitrarily given initial value, converges to the set consisting of the equilibrium points of the neural network, whose elements are all the optimal solutions of the primal constrained optimization problem. In particular, we give the condition that the equilibrium point set of the neural network coincides with the optimal solution set of the primal constrained optimization problem and the condition ensuring convergence to the optimal solution set in finite time. Furthermore, illustrative examples show the correctness of the results in this paper, and the good performance of the proposed neural network. [ABSTRACT FROM AUTHOR]

A new dynamical system and computational circuit is described and analyzed. The dynamics permits the construction of a Lyapunov function that ensures global convergence to a unique stable equilibrium. The analog circuit realization is of the neural network type, with N cells represented by high-gain amplifiers, global feedback, and at most 2N interconnections, where N is the number of inputs. A specific application (called "the K-selector") which signals the ranks of the K largest elements of input list and, in parallel the rank of the (K + 1)th element, is designed and numerically tested. For a given density of the input elements, one obtains feasible separation intervals of output signals, i.e., good processing performances. The circuit requires an appropriate control source and suitable scaling of the input data. [ABSTRACT FROM AUTHOR]