Article ID: | iaor20133824 |
Volume: | 77 |
Issue: | 2 |
Start Page Number: | 227 |
End Page Number: | 237 |
Publication Date: | Apr 2013 |
Journal: | Mathematical Methods of Operations Research |
Authors: | Zalinescu C, Voisei M |
Keywords: | duality, global optimization |
The main goal of this note is to give a counterexample to the Triality Theorem in Gao and Ruan (Math Methods Oper Res 67:479–491, 2008). This is done first by considering a more general optimization problem with the aim to encompass several examples from Gao and Ruan (Math Methods Oper Res 67:479–491, 2008) and other papers by Gao and his collaborators (see f.i. Gao Duality principles in nonconvex systems. Theory, methods and applications. Kluwer, Dordrecht, 2000; Gao and Sherali Advances in applied mathematics and global optimization. Springer, Berlin, 2009). We perform a thorough analysis of the general optimization problem in terms of local extrema while presenting several counterexamples.