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Counterexamples to a triality theorem for quadratic-exponential minimization problems

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  • M. Voisei
  • C. Zălinescu

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

Suggested Citation

  • M. Voisei & C. Zălinescu, 2013. "Counterexamples to a triality theorem for quadratic-exponential minimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(2), pages 227-237, April.
    • Handle: RePEc:spr:mathme:v:77:y:2013:i:2:p:227-237
    DOI: 10.1007/s00186-012-0426-1
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    References listed on IDEAS

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    1. David Gao & Ning Ruan, 2008. "Solutions and optimality criteria for nonconvex quadratic-exponential minimization problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(3), pages 479-491, June.
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