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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]

Dynamic security region (DSR) for security assessment and preventive control is defined in terms of variables that are under the control of the dispatcher prior to a fault. The boundary of DSR can be expressed using the function describing the stable manifold of the controlling unstable equilibrium point. The function is shown to be the solution of a partial differential equation. Quadratic and linear approximations to the function characterizing the boundary of DSR are derived. Numerical tests of the approximations are conducted. Potential applications of the method are discussed. [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]

Cellular neural networks (CNNs) are dynamical systems, described by a large set of coupled nonlinear differential equations. The equilibrium-point analysis is an important step for understanding the global dynamics and for providing design rules. We yield a set of sufficient conditions (and a simple algorithm for checking them) ensuring the existence of at least one stable equilibrium point. Such conditions give rise to simple constraints, that extend the class of CNNs, for which the existence of a stable equilibrium point is rigorously proved. In addition, they are suitable for design and easy to check, because they are directly expressed in term of the template elements. [ABSTRACT FROM AUTHOR]