论文标题
用于解决逆准变量不平等的神经网络
A Neural Network for Solving Inverse Quasi-Variational Inequalities
论文作者
论文摘要
我们研究解决逆变量不平等问题的解决方案的存在和唯一性。通过神经网络方法解决优化问题，例如变异不平等，单调包含和逆变异问题，我们考虑了与逆变量不平等问题相关的神经网络，并确定对所提出的网络的解决方案的存在和独特性。我们证明，所提出的神经网络的每一个轨迹都会收敛到逆准变量不平等问题的独特解决方案，并且该网络在其平衡点上是全球渐近稳定的。我们还证明，如果控制逆变量不平等问题的函数是强烈单调的，Lipschitz连续不断，那么该网络在其平衡点上的全球指数稳定。我们将网络离散化，并表明通过网络离散化生成的序列在某些关于所涉及的参数的假设下，将网络离散化强烈收敛到逆准差异不平等问题的解决方案。最后，我们提供数值示例来支持和说明我们的理论结果。
We study the existence and uniqueness of solutions to the inverse quasi-variational inequality problem. Motivated by the neural network approach to solving optimization problems such as variational inequality, monotone inclusion, and inverse variational problems, we consider a neural network associated with the inverse quasi-variational inequality problem, and establish the existence and uniqueness of a solution to the proposed network. We prove that every trajectory of the proposed neural network converges to the unique solution of the inverse quasi-variational inequality problem and that the network is globally asymptotically stable at its equilibrium point. We also prove that if the function which governs the inverse quasi-variational inequality problem is strongly monotone and Lipschitz continuous, then the network is globally exponentially stable at its equilibrium point. We discretize the network and show that the sequence generated by the discretization of the network converges strongly to a solution of the inverse quasi-variational inequality problem under certain assumptions on the parameters involved. Finally, we provide numerical examples to support and illustrate our theoretical results.
