This paper introduces a class of discrete-time recurrent neural networks designed to solve variational inequalities and related optimization problems subject to linear equalities and bound constraints. This discrete-time network is an extension of previously proposed continuous-time recurrent neural networks. The discrete-time analog of the corresponding continuous-time model is formulated using the Euler discretization method. Sufficient conditions are provided to guarantee that the output variables of the discrete-time network are convergent to optimal solutions in finite time. In the proposed approach, the neural network structure is based on the Karush-Kuhn-Tucker (KKT) optimality conditions. Instead of employing commonly used activation functions, the KKT multipliers are treated as control inputs and implemented with finite time stabilizing terms based on equivalent control and unit control methods. The main advantage of the proposed discrete-time network lies in its fixed number of parameters regardless of the problem dimension. This characteristic allows the network to scale easily from lower to higher dimensions. Finally, simulation results on numerical examples are discussed to demonstrate the effectiveness and performance of the discrete-time network.