Nonlinear Analysis: Theory, Methods & Applications
Global Optimization with Polynomials and the Problem of Moments
SIAM Journal on Optimization
Journal of Global Optimization
Canonical Duality Theory and Solutions to Constrained Nonconvex Quadratic Programming
Journal of Global Optimization
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Counterexamples to some triality and tri-duality results
Journal of Global Optimization
Journal of Global Optimization
Journal of Global Optimization
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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.