Neighboring Local Optimal Solutions and Its Applications

Chapter

Abstract

The number of neighboring local optimal solutions is an important index for assessing the complexity of nonlinear systems and the computational complexity of numerical methods for nonlinear optimization. Sperner’s lemma provides an effective tool for this quantitative study. It has been shown that, in general there are at least 2n local-optimal solutions neighboring to any given one, for a class of nonlinear optimization problems. Furthermore, if a collection of neighboring local-optimal solutions retains the local-independence, then each solution must have at least n(n + 1) neighboring local-optimal solutions instead. The local-independence has been justified for the planar case at the end.

Keywords

Nonlinear optimization Local optimal solution Lower bound 

Notes

Acknowledgements

The presented work was partially supported by the CERT through the National Energy Technology Laboratory Cooperative Agreement No. DE-FC26-09NT43321, and partially supported by the National Science Foundation, USA, under Award #1225682.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.School of Electrical and Computer EngineeringCornell UniversityIthacaUSA

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