A systematic search method for obtaining multiple local optimal solutions of nonlinear programming problems

We propose, in this paper, a systematic method to find several local optimal solutions for general nonlinear optimization problems. We have developed some analytical results for quasi-gradient systems and reflected gradient systems, applying these results to derive topological and geometric properties of the critical points of the underlying objective function. A mechanism has also been devised to escape from a local optimal solution and proceed into another local optimal solution via decomposition points. By properly switching between quasi-gradient systems and reflected gradient systems, our proposed method can attain a set of local optimal solutions. The proposed method is applied to two test examples with promising results.