One-step and multistep procedures for constrained minimization problems

One approach to solving general smooth minimization problems is to integrat e an ordinary differential equation appropriate to the underlying minimizat ion problem. Tn the present paper we derive a global convergence result for smooth minimization problems via discretizing such a corresponding dynamic al system using an arbitrary one- or linear multistep method with constant step size. In addition, we compare the asymptotic features of the numerical and exact solutions.