A method for obtaining a global optimal solution of general nonlinear programming problems includes the steps of first finding, in a deterministic manner, all stable equilibrium points of a nonlinear dynamical system that satisfies conditions (C1) and (C2), and then finding from said points a global optimal solution. A practical numerical method for reliably computing a dynamical decomposition point for large-scale systems comprises the steps of moving along a search path .phi..sub.t(x.sub.s).ident.{x.sub.s+ t.times.s, t.epsilon..sup.+} starting from x.sub.s and detecting an exit point, x.sub.ex, at which the search path .phi..sub.t(x.sub.s) exits a stability boundary of a stable equilibrium point x.sub.s using the exit point x.sub.ex as an initial condition and integrating a nonlinear system to an equilibrium point x.sub.d, and computing said dynamical decomposition point with respect to a local optimal solution x.sub.s wherein the search path is x.sub.d.