A trajectory based method is suggested. The method differs conceptually from the gradient methods in that the minimization problem is solved via consideration of the analogous physical problem of the motion of a particle in a conservative force field. The potential energy of the particle is represented by the function to be minimized. The method proposed simulates the motion of the particle by monitoring its potential and kinetic energies. The motion of the particle can be represented by a system of second order nonlinear ordinary differential equations where the state and co-state variables are represented by primal and dual variables, respectively. The iterative process involves the solution of the system of equations via a method known as ``leap-frog". Extensive numerical results are presented showing the robustness of the method. Convergence properties are being investigated.