Counterexamples to a triality theorem for quadratic‐exponential minimization problems

Counterexamples to a triality theorem for quadratic‐exponential minimization problems

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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: ,
Keywords: duality, global optimization
Abstract:

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.

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