One-step and multistep procedures for constrained minimization problems

Abstract

One approach to solving general smooth minimization problems is to integrate an ordinary differential equation appropriate to the underlying minimization problem. In the present paper we derive a global convergence result for smooth minimization problems via discretizing such a corresponding dynamical 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.