## Complete solutions and extremality criteria to polynomial optimization problems (2006)

Venue: | Journal of Global Optimization |

Citations: | 10 - 3 self |

### BibTeX

@ARTICLE{Gao06completesolutions,

author = {David Yang Gao},

title = {Complete solutions and extremality criteria to polynomial optimization problems},

journal = {Journal of Global Optimization},

year = {2006},

volume = {35},

pages = {131--143}

}

### OpenURL

### Abstract

Abstract. 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 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. Key words: critical point theory, duality, global optimization, nonlinear programming, NP-hard problem, polynomial minimization.