ABSTRACT In 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.

中文翻译：

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一种用于解决凸二阶锥约束变分不等式问题的新神经网络框架，并在多指机器人手中应用

摘要在本文中，我们考虑了一种新的神经网络模型来简单地解决凸二阶锥约束变分不等式问题。基于平滑方法，变分不等式 (VI) 问题首先转换为凸二阶锥规划 (CSOCP)。使用高性能模型，求解得到的凸规划问题。根据凸优化的Karush-Kuhn-Tucker条件，证明了所提出的神经网络的平衡点等价于CSOCP问题的最优解。通过采用李雅普诺夫函数方法，还表明所提出的神经网络模型在李雅普诺夫意义上是稳定的，并且全局收敛于原始优化问题的精确最优解。