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Solutions and optimality criteria for nonconvex quadratic-exponential minimization problem

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  • David Gao
  • Ning Ruan

Abstract

This paper presents a set of complete solutions and optimality conditions for a nonconvex quadratic-exponential optimization problem. By using the canonical duality theory developed by the first author, the nonconvex primal problem in n-dimensional space can be converted into an one-dimensional canonical dual problem with zero duality gap, which can be solved easily to obtain all dual solutions. Each dual solution leads to a primal solution. Both global and local extremality conditions of these primal solutions can be identified by the triality theory associated with the canonical duality theory. Several examples are illustrated. Copyright Springer-Verlag 2008

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:67:y:2008:i:3:p:479-491
    DOI: 10.1007/s00186-007-0204-7
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    Cited by:

    1. Linsong Shen & Yanjun Wang & Xiaomei Zhang, 2016. "Robust canonical duality theory for solving nonconvex programming problems under data uncertainty," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(1), pages 183-204, August.
    2. 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.

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