Solutions and optimality criteria for nonconvex quadratic-exponential minimization problem

David Yang Gao, Ning Ruan

Research output: Contribution to journalArticleResearchpeer-review

12 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)479-491
Number of pages13
JournalMathematical Methods of Operations Research
Issue number3
Publication statusPublished - Jun 2008
Externally publishedYes


  • Duality theory
  • Global optimization
  • Nonconvex programming
  • Nonlinear algebraic equation
  • Quadratic-exponential function
  • Triality

Cite this