Abstract
This article corrects the results presented in [7] (D.Y. Gao and Wei-Chi, Yang, Optimization, 57(5), 705–714, 2008) which were challenged in [13] (M.D. Voisei, C. Zalinescu, Optimization, 60(5), 593–602, 2011). We aim to use the points of view presented in [13] (M.D. Voisei, C. Zalinescu, Optimization, 60(5), 593–602, 2011) to modify the original results and highlight that the consideration of the Gao–Strang total complementary function and the canonical duality theory are indeed quite useful for solving a class of real-world global optimization problems with nonconvex constraints. Additionally, we demonstrate how a perturbed canonical dual method can be used to solve the counter example presented in [13] (M.D. Voisei, C. Zalinescu, Optimization, 60(5), 593–602, 2011) which has multiple global minimum solutions.
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Notes
- 1.
R. Parris: Peanut Software Homepage: http://math.exeter.edu/rparris/, Version 1.54 (2012).
- 2.
See Maxima.sourceforge.net. Maxima, a Computer Algebra System. Version 5.22.1 (2010). http://maxima.sourceforge.net/.
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Acknowledgements
This research is supported by US Air Force Office of Scientific Research under the grants FA2386-16-1-4082 and FA9550-17-1-0151. Comments and suggestions from several anonymous referees are sincerely acknowledged.
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Morales-Silva, D., Gao, D.Y. (2017). On Minimal Distance Between Two Surfaces. In: Gao, D., Latorre, V., Ruan, N. (eds) Canonical Duality Theory. Advances in Mechanics and Mathematics, vol 37. Springer, Cham. https://doi.org/10.1007/978-3-319-58017-3_18
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