A trajectory-based methodology for systematically computing multiple optimal solutions of general nonlinear programming problems

In this paper, we propose a novel trajectory-based methodology for systematically computing multiple optimal solutions of general nonlinear programming problems. The objective functions are assumed to be twice-differentiable and the feasible region may be non-convex and disconnected. A theoretical foundation of the methods is made on the basis of the theory of differential topology and the qualitative theory of dynamical systems. Our proposed method begins with an arbitrary initial point and consists of two distinct main phases: Phase I systematically finds several or all of the different connected feasible regions from the initial point. Phase II then finds multiple or all of the local minima in each feasible region obtained in Phase I. A numerical example is shown to illustrate the proposed method