Continuous Approximation of Nonlinear L1 Problem Based on BP Neural Network

Abstract

The nonlinear L1 problem is a non-differentiable optimization problem. The objective function of nonlinear L1 problem is continuously approximated by using the characteristics of neural network in order to make it continuously differentiable. A concrete algorithm for approximation of continuous functions at the discontinuity of the objective function is given based on the principles of BP neural network, and then the effectiveness of the method is verified by a specific example.