Global solution of nonlinear programming problem with equality and inequality constraints ViaDifferential equation Approach

The numerical solution of nonlinear programming problem with equality and inequality constraints based on the theoretical aspects has been developed using a suitable nonlinear autonomous differential system. Nonlinear autonomous differential system is introduced as the base of the theory instead of the usual approaches, and the relation between the critical points and local optima of the original optimization problem has been proved and presented. Asymptotic stability of the critical points (optimum) optima has also been proved and discussed. A numerical algorithm which has capable of finding (local) global optima depending on the nature of trajectory and critical point as well as their behavior has been presented. The numerical algorithm has been illustrated for different example to show its efficiency.