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Hopfield和Tank证明几种最优化问题能用Hopfield网络快速求解,而Hopfield网络是简单的类似神经元模拟处理机的递推网络。使用Hopfield网络时,目标函数的自变量收敛于超立方体的顶点。因此,它们的应用严格地限于决策最优化问题。在本文中,我们将研究目标函数自变量是实数的问题。基于Hopfield网络的概念,推导了求解最小二乘估计问题的神经网络。用这个网络,目标函数可能收敛于超立方体内的任何点,给出一个具有极大速度的实值解。由于所选择的能量函数的凸状性质,不会出现收敛到局部最小值的问题。我们还介绍了空间迭代搜索方法,以便找到可能存在于空间内任意点的最优解。最后,给出了求解线性系统和参数估计问题的模拟结果。
Hopfield and Tank prove that several kinds of optimization problems can be solved quickly by Hopfield network, which is a simple recursive network similar to neuron simulation processor. When using Hopfield network, the arguments of the objective function converge to the vertices of the hypercube. Therefore, their application is strictly limited to decision-making optimization problems. In this paper, we will study the problem that the objective function argument is a real number. Based on the concept of Hopfield network, the neural network for solving the least square estimation problem is deduced. With this network, the objective function may converge at any point in the hypercube, giving a real-valued solution with a very large velocity. Due to the convex nature of the energy function chosen, there is no problem of converging to a local minimum. We also introduce spatial iterative search methods to find the optimal solution that may exist at any point in space. Finally, the simulation results for solving linear systems and parameter estimation problems are given.