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

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2 Author(s)
Hsiao-Dong Chiang ; Sch. of Electr. Eng., Cornell Univ., Ithaca, NY, USA ; Chia-Chi Chu

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

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IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications  (Volume:43 ,  Issue: 2 )