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._t(x_s)={x_s+ t x s, t.epsilon⁺} starting from x_s and detecting an exit point, x_ex, at which the search path .phi._t(x_s) exits a stability boundary of a stable equilibrium point x_s using the exit point x_ex as an initial condition and integrating a nonlinear system to an equilibrium point x_d, and computing said dynamical decomposition point with respect to a local optimal solution x_s wherein the search path is x_d.

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