Abstract: The optimization problem is discussed, in which its objective function can be decomposed into one convex function minus one generalized differential function. For a given approximate value of optimal solution, the differential function is approximated locally at the current approximate value by a linear function, which leads to an approximation of the objective function. After solving the approximation of the objective function, the next（often better）approximate solution for the objective function can be found. The above process is repeated until it satisfies some specified convergent criterion. The global convergence of designing an optimal algorithm can be proven, which is useful for solving smooth or non-smooth optimal problem and analysing the stability of Hopfield network.