Neural Network for Solving SOCQP and SOCCVI Based on Two Discrete-Type Classes of SOC Complementarity Functions

This paper focuses on solving the quadratic programming problems with second-order cone constraints (SOCQP) and the second-order cone constrained variational inequality (SOCCVI) by using the neural network. More specifically, a neural network model based on two discrete-type families of SOC complementarity functions associated with second-order cone is proposed to deal with the Karush-Kuhn-Tucker (KKT) conditions of SOCQP and SOCCVI. The two discrete-type SOC complementarity functions are newly explored. The neural network uses the two discrete-type families of SOC complementarity functions to achieve two unconstrained minimizations which are the merit functions of the Karuch-Kuhn-Tucker equations for SOCQP and SOCCVI. We show that the merit functions for SOCQP and SOCCVI are Lyapunov functions and this neural network is asymptotically stable. The main contribution of this paper lies on its simulation part because we observe a different numerical performance from the existing one. In other words, for our two target problems, more effective SOC complementarity functions, which work well along with the proposed neural network, are discovered.