We present iterative methods for finding the critical points and/or the minima of extended real valued functions of the form $\phi = \psi+ g-h$, where $\psi$ is a differentiable function and g and h are convex, proper, and lower semicontinuous. The underlying idea relies upon the discretization of a first order dissipative dynamical system which allows us to preserve the local feature and to obtain some convergence results. The main theorems not only recover known convergence results in this field but also provide a theoretical basis for the development of new iterative methods.