一类线性约束非线性规划的初始神经网络

New primal neural networks for solving a class of nonlinear programs with linear constraints

目的 建立求解一类线性约束非线性凸规划的简单可行的神经网络。方法 射影方法和Lyapunov直接方法。结果 基于问题自身的结构特点和射影方法,提出了求解一类线性约束非线性凸规划的两个神经网络模型。定义了Lyapunov函数,严格证明了它们是渐近稳定的。此外,在一定的条件下证明了其指数稳定性。新模型的规模均与原问题相同,不含任何参数,并且其稳定性不需要Lipschitz条件,模拟实验表明新模型不仅可行,而且有效。结论 建立了求解一类线性约束非线性凸规划的两个简单可行的初始神经网络,并在适当的条件下分别证明了其渐近稳定性和指数稳定性。

AimTo construct the simple and feasible neural networks for solving a class of linearly constrained convex programming problems.MethodsThe projection method and Lyapunov′s direct method.ResultsTwo primal neural-network models for solving a class of linearly constrained convex programming problems are proposed by means of their inherent properties and the projection method. The proposed models have been strictly shown to be asymptotically stable by defining their Lyapunov functions.Furthermore,the global exponential stability of the proposed neural networks is also proved under mild conditions.New models have the same size as the original problem,no Lipschitz condition and no extra parameter.The feasibility and effectiveness of the proposed neural networks are supported by the simulation experiments.ConclusionTwo simple and feasible primal neural-network models for solving a calss of linearly constrained convex programming problems are constructed,and their asymptotic stability and the global exponential stability are proved under mild conditions,respectively.