Abstract:

In order to seek to optimal solution satisfying the necessary conditions of optimality, aiming at the optimization problems that objective functions are nonLipschitz and the feasible region consists of linear inequality or nonlinear inequality, we design a new smooth neural network by the penalty function method and the smoothing approximate techniques which convert nonsmoothing objective functions into smoothing functions. Detailed theoretical analysis proves the uniform boundedness and globality of the solutions to smooth neural networks, regardless of the initial points inside or outside of the feasible domain. Moreover, any accumulation point of the solutions of to smooth neural networks is a stationary point of the optimization promble. Numerical examples also demonstrate the effectiveness of the method.

Key words: non-Lipschitz , function;smoothing approximate techniques;stationary point;accumulation point