An application of a merit function for solving convex programming problems

•The main idea is to convert the CNP problem based on a merit function into an equivalent unconstrained minimization problem.•A gradient model is then defined directly using the derivatives of the energy function.•The proposed dynamic model is proved to be stable in the sense of Lyapunov.•The model is globally convergent to an exact optimal solution of the problem.•The validity of the model is demonstrated by using several examples.

This paper presents a gradient neural network model for solving convex nonlinear programming (CNP) problems. The main idea is to convert the CNP problem into an equivalent unconstrained minimization problem with objective energy function. A gradient model is then defined directly using the derivatives of the energy function. It is also shown that the proposed neural network is stable in the sense of Lyapunov and can converge to an exact optimal solution of the original problem. It is also found that a larger scaling factor leads to a better convergence rate of the trajectory. The validity and transient behavior of the neural network are demonstrated by using various examples.