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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Zhu, J., Zhao, S., Liu, G.: Solution to global minimization of polynomials by backward differential flow. J. Optim. Theory Appl. 161, 828–836 (2014)
Arnold, V.I.: Ordinary Differential Equations. The MIT Press, Cambridge (1978)
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Arıkan, O., Burachik, R.S. & Kaya, C.Y. “Backward Differential Flow” May Not Converge to a Global Minimizer of Polynomials. J Optim Theory Appl 167, 401–408 (2015). https://doi.org/10.1007/s10957-015-0727-7
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DOI: https://doi.org/10.1007/s10957-015-0727-7