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发展了Leung等人所提出的解决非线性凸规划问题的动态反馈神经网络模型,引入基于次梯度动态反馈神经网络模型解决非可微凸优化问题.对于无约束非可微凸优化问题,假定目标函数是强迫性的凸函数,证明了由投影次梯度构造的反馈神经网络轨道从任意初值点出发都收敛于一个渐近稳定的平衡点,该平衡点为原无约束问题的最优解.对于约束非可微凸优化问题,在目标函数是强迫性的凸函数,约束函数也具有凸性的假定下,依次造构能量函数序列和相应的基于次梯度的动态反馈子网络的模型,建立了收敛定理并给出了停时条件.最后,设计了两种有效的算法并结合一些实例进行了仿真验证.
The dynamic feedback neural network model proposed by Leung et al. To solve the nonlinear convex programming problem is developed and a non-asymptotically convex optimization problem is introduced based on the sub-gradient dynamic feedback neural network model. For the unconstrained non-astigmatic convex optimization problem, Function is a forcing convex function. It is proved that the feedback neural network constructed by projection sub-gradient converges to an asymptotically stable equilibrium point from any initial point, which is the optimal solution of the original unconstrained problem. For constrained non-askew-convex optimization problems, under the assumption that the objective function is a forcing convex function and the restraining function also has convexity, the energy function sequence and the corresponding sub-gradient-based dynamic feedback sub-network model are constructed in turn The convergence theorem is given and the stopping condition is given.Finally, two effective algorithms are designed and simulated with some examples.