Design of a kind of nonlinear neural networks for solving the inverse optimal value problem with convex constraints

作者：Wu Huaiqin^*; Wang Kewang; Guo Qiangqiang; Xu Guohua; Li Ning

来源：International Journal of Machine Learning and Cybernetics, 2014, 5(1): 85-92.

DOI：10.1007/s13042-012-0138-0

• Neural networks
• Bilevel programming
• Inverse optimal value problem
• Global asymptotical stability
• Fish-Burmeister function

In this paper, we consider how to design a kind of nonlinear neural networks for solving the inverse optimal value problem with convex constraints. Firstly, based on optimal theory, the inverse optimal value problem considered is changed to a class of nonlinear bilevel program problems. Secondly, under the given assumptions, the corresponding nonlinear bilevel programming problem can be reduced to the one-level programming problem. Thirdly, based on the gradient theory, a nonlinear neural network model is designed to solve this one-level programming problem. Moreover, by employing Lyapunov function approach, the proposed neural network is analyzed to be globally Lyapunov stable and capable of generating approximal optimal solution to the inverse optimal value problem. Finally, two illustrative examples are provided to verify the feasibility and the efficiency of the proposed method.

• 出版日期2014-2
• 单位燕山大学