Real Radicals and Finite Convergence of Polynomial Optimization Problems

  • Yoshiyuki SekiguchiEmail author
Research Article
Part of the Advances in Mathematical Economics book series (MATHECON, volume 20)


Polynomial optimization appears various areas of mathematics. Although it is a fully nonlinear nonconvex optimization problems, there are numerical algorithms to approximate the global optimal value by generating sequences of semidefinite programming relaxations. In this paper, we study how real radicals of ideals have roles in duality theory and finite convergence property. Especially, duality theory is considered in the case that the truncated quadratic module is not necessarily closed. We will also try to explain the results by giving concrete examples.


Polynomial optimization Real radicals Sums of squares Moment problems 


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Copyright information

© Springer Science+Business Media Singapore 2016

Authors and Affiliations

  1. 1.Graduate School of Marine Science and TechnologyTokyo University of Marine Science and TechnologyTokyoJapan

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