Counter-examples in bi-duality, triality and tri-duality
Radu Strugariu, M. D. Voisei, Constantin Zălinescu · Discrete and Continuous Dynamical Systems · 2011
In this paper, by providing simple counterexamples, severalimportant results in bi-duality, triality and tri-duality, anoptimization 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 subsequentpapers by D.Y. Gao and his collaborators are analyzed, false claimsare exposed and when possible corrected, while the possibility orimpossibility of obtaining correct various alternatives to theclassical minimax relations are discussed.