Counterexamples to a triality theorem for quadratic-exponential minimization problems

M. Voisei () and C. Zălinescu ()

Mathematical Methods of Operations Research, 2013, vol. 77, issue 2, 227-237

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. Copyright Springer-Verlag Berlin Heidelberg 2013

Keywords: Counterexample; Nonconvex programming; Triality (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s00186-012-0426-1

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