参数线性规划问题的新型光滑精确罚函数神经网络

摘要

In view of solving linear programming problems with parameters both in objective function and constraints, a computational method based on novel smooth exact penalty function neural networks is proposed. First, the error function is introduced to constructing the approximate function of unit step function, which is used to give the smooth penalty function that more accurately approximates the L1 exact penalty function, and its basic properties are discussed. Second, the neural network model for parameter linear programming problems is constructed based on the proposed smooth exact penalty function and the stability and convergence of the neural networks are proved. Moreover, the specific calculation steps of our proposed neural network model for the optimization are given. Finally, a numerical example is given to illustrate that the proposed method possesses the smaller penalty factor, easier construction and higher accuracy.%针对不等式约束条件下，目标函数和约束条件中含有参数的线性规划问题，提出一种基于新型光滑精确罚函数的神经网络计算方法。引入误差函数构造单位阶跃函数的近似函数，给出一种更加精确地逼近于 L1精确罚函数的光滑罚函数，讨论了其基本性质；利用所提光滑精确罚函数建立了求解参数线性规划问题的神经网络模型，证明了该网络模型的稳定性和收敛性，并给出了详细的算法步骤。数值仿真验证了所提方法具有罚因子取值小、结构简单、计算精度高等优点。