A new neural network framework for solving convex second-order cone constrained variational inequality problems with an application in multi-finger robot hands

Abstract

ABSTRACTIn this paper, we consider a new neural network model to simply solve the convex second-order cone constrained variational inequality problem. Based on a smoothing method, the variational inequality (VI) problem is first converted to a convex second-order cone programming (CSOCP). Using a high-performance model, the obtained convex programming problem is solved. According to Karush-Kuhn-Tucker conditions of convex optimisation, the equilibrium point of the proposed neural network is proved to be equivalent to the optimal solution of the CSOCP problem. By employing Lyapunov function approach, it is also shown that the presented neural network model is stable in the sense of Lyapunov and it is globally convergent to an exact optimal solution of the original optimisation problem. The capability of the method is demonstrated by several numerical results.