“Backward differential flow” may not converge to a global minimizer of polynomials

Date
2015
Advisor
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Instructor
Source Title
Journal of Optimization Theory and Applications
Print ISSN
0022-3239
Electronic ISSN
Publisher
Springer New York LLC
Volume
167
Issue
1
Pages
401 - 408
Language
English
Type
Article
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Abstract

We provide a simple counter-example to prove and illustrate that the backward differential flow approach, proposed by Zhu, Zhao and Liu for finding a global minimizer of coercive even-degree polynomials, can converge to a local minimizer rather than a global minimizer. We provide additional counter-examples to stress that convergence to a local minimum via the backward differential flow method is not a rare occurence.

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Book Title
Keywords
Global optimization, Polynomial optimization, Trajectory methods
Citation
Published Version (Please cite this version)