Journal of Global Optimization

, Volume 35, Issue 1, pp 131–143 | Cite as

Complete Solutions and Extremality Criteria to Polynomial Optimization Problems

  • David Yang Gao


This paper presents a set of complete solutions to a class of polynomial optimization problems. By using the so-called sequential canonical dual transformation developed in the author’s recent book [Gao, D.Y. (2000), Duality Principles in Nonconvex Systems: Theory, Method and Applications, Kluwer Academic Publishers, Dordrecht/Boston/London, xviii + 454 pp], the nonconvex polynomials in \(\mathbb{R}^n\) can be converted into an one-dimensional canonical dual optimization problem, which can be solved completely. Therefore, a set of complete solutions to the original problem is obtained. Both global minimizer and local extrema of certain special polynomials can be indentified by Gao-Strang’s gap function and triality theory. For general nonconvex polynomial minimization problems, a sufficient condition is proposed to identify global minimizer. Applications are illustrated by several examples.


critical point theory duality global optimization nonlinear programming NP-hard problem polynomial minimization 


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Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Department of MathematicsVirginia Polytechnic Institute & State UniversityBlacksburgUSA

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