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This paper aims to present a new class of recurrent neural networks based on projection operators for solving variational inequalities and related optimization problems subject to linear equalities and bound constraints. In the proposed approach, the neural network structure is based on the Karush–Kuhn–Tucker (KKT) optimality conditions. Instead of commonly used activation functions, the KKT multipliers are considered control inputs and implemented with finite time stabilizing terms based on unit control. The output variables of the neural network are proven to be stable in the sense of Lyapunov and convergent to optimal solutions in finite time. In addition, a methodology based on the particle swarm optimization (PSO) algorithm is presented for the optimal selection of network design parameters. The main advantage of the proposed neural network is its fixed number of parameters regardless of problem dimension, enabling the network to be easily scalable from a lower to a higher dimension. Finally, simulation results of numerical examples are provided to illustrate the effectiveness and performance of the proposed neural network. [Display omitted] • Convergence to optimal solutions in finite time. • Neural network with a fixed number of parameters regardless of the problem dimension. • Design of activation functions that enforce a sliding mode. • PSO-based methodology for optimal selection of the neural network design parameters. [ABSTRACT FROM AUTHOR]

In this paper, we propose two kinds of prediction–correction methods, discrete-time Euler-smoothing methods, for solving the general time-varying convex constrained optimization problem. By using the complementarity function and smoothing technique, the Karush–Kuhn–Tucker (KKT) trajectory of the problem can be reformulated as a system of smooth equations and considering the dynamics of the system of smooth equations in a discrete constant time-sampling periods scheme. The proposed methods mainly consist of the prediction step derived by Euler approximation and the correction step generated by one or multiple Newton iterations. Under some reasonable conditions, the approximate solution trajectories produced by the methods achieve the asymptotic error bound behaving as O (h 4) with respect to optimal trajectory both in the primal and dual space as the smoothing parameter approaches to zero, where h is the sampling period. Finally, the experimental results show that our methods are efficient, and the steady-state tracking errors are much smaller than the other prediction–correction methods under the same conditions. [ABSTRACT FROM AUTHOR]