Abstract: In this paper, based on neural network, an approach of solving interval quadratic programming problems with linear constraints is proposed. By using augmented Lagrange function, a neural network for solving quadratic programming is presented. Based on Saddle point theorem, the equilibrium point of the proposed neural network is proved to be equivalent to the optimal solution of the interval quadratic programming problems. The global exponential stability of the proposed neural network is analyzed in terms of a Lyapunov approach. Two illustrative examples are provided to illustrate the usefulness and the efficiency of the theoretical results.

Key words: interval quadratic programming, neural network, augmented lagrange function, lyapunov function

摘要： 在本文中,基于神经网络,提出了一类求解具有线性约束区间二次规划问题的方法,使用增广拉格朗日函数,建立了求解规划问题的神经网络模型。基于压缩不动点理论,证明了所提出神经网络的平衡点就是等式约束区间二次规划问题的最优解。使用适当的Lyapunov函数,证明了所提出的神经网络的平衡点是全局指数稳定的。最后,两个数值仿真结果验证了本文所用方法的可行性与有效性。

关键词: 区间二次规划, 神经网络, 增广拉格朗日函数, Lyapunov函数