Abstract

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 φt(xs)≡{xs+ t×ŝ, tε+} starting from xs and detecting an exit point, xex, at which the search path φt(xs) exits a stability boundary of a stable equilibrium point xs using the exit point xex as an initial condition and integrating a nonlinear system to an equilibrium point xd, and computing said dynamical decomposition point with respect to a local optimal solution xs wherein the search path is xd.