Neighboring Local Optimal Solutions and Its Applications

Hsiao-Dong Chiang () and Tao Wang ()
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Hsiao-Dong Chiang: Cornell University, School of Electrical and Computer Engineering
Tao Wang: Cornell University, School of Electrical and Computer Engineering

A chapter in Mathematics Without Boundaries, 2014, pp 117-138 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4939-1124-0_5

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DOI: 10.1007/978-1-4939-1124-0_5

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