Analog circuits for solving a class of variational inequality problems

In this paper, we present the analog circuits to solve a class of variational inequality problems (VIPs) based on the projection neural network (PNN) and inertial projection neural network (IPNN) algorithms. The proposed circuits are normative and only require basic circuit elements. The optimal solutions of VIPs are equivalent to the stable output voltages of the associated circuits. This paper also shows how to design analog circuits with projection operators (box constrains set and sphere constrains set) on the basis of PNN and IPNN algorithms. As a result, a class of variational inequality problems can be solved by proposed circuit frameworks. The effectiveness and superiority (with less computing time) of the proposed analog circuits are expound by simulating on three examples.