Abstract
In this paper, by providing simple counterexamples, several important results in bi-duality, triality and tri-duality, an optimization theory established and presented by D.Y. Gao in his book Duality Principles in Nonconvex Systems. Theory, Methods and Applications, Kluwer Academic Publishers, Dordrecht, 2000, are proven to be false. Other results concerning this optimization theory from subsequent papers by D.Y. Gao and his collaborators are analyzed, false claims are exposed and when possible corrected, while the possibility or impossibility of obtaining correct various alternatives to the classical minimax relations are discussed.
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