Abstract
The aim of this paper is to show that the results on triality and tri-duality in Gao (J Glob Optim 17:127–160, 2000; J Glob Optim 29:377–399, 2004; J Glob Optim 35:131–143, 2006; Encyclopedia of optimization, 2nd edn. Springer, New York, pp 822–828, 2009) and Gao et al. (J Glob Optim 45:473–497, 2009) are false. To prove this we provide simple counterexamples.
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References
Gao D.Y.: Duality Principles in Nonconvex Systems. Theory, Methods and Applications. Kluwer, Dordrecht (2000)
Gao D.Y.: Canonical dual transformation method and generalized triality theory in nonsmooth global optimization. J. Glob. Optim. 17, 127–160 (2000)
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Gao D.Y.: Complete solutions and extremality criteria to polynomial optimization problems. J. Glob. Optim. 35, 131–143 (2006)
Gao D.Y., Ruan N., Sherali H.D.: Solutions and optimality criteria for nonconvex constrained global optimization problems with connections between canonical and Lagrangian duality. J. Glob. Optim. 45, 473–497 (2009)
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Voisei, M.D., Zălinescu, C. Counterexamples to some triality and tri-duality results. J Glob Optim 49, 173–183 (2011). https://doi.org/10.1007/s10898-010-9592-y
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DOI: https://doi.org/10.1007/s10898-010-9592-y