The novel characteristics for training Ridge Polynomial neural network based on Lagrange multiplier

Abstract

In this paper, the Lagrange multiplier is presented to train the Ridge Polynomial neural network, for improving the convergence rate and avoiding the ill-conditioned problem (penalty factor must go to infinity). In the process of training this network, with this method, the constrained problem is successfully transformed into an unconstrained problem. Based on the two assumptions, we propose the necessity theorem, the linear convergence theorem and the stability theorem for the property of weights iteration. Finally, the experimental results demonstrate that the proposed theorems are valid, and the effectiveness of convergence speed is confirmed.

Keywords

• Ridge Polynomial neural network
• Lagrange multiplier
• Necessity
• Linear convergence
• Stability