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2016 | OriginalPaper | Buchkapitel

Real Radicals and Finite Convergence of Polynomial Optimization Problems

verfasst von : Yoshiyuki Sekiguchi

Erschienen in: Advances in Mathematical Economics Volume 20

Verlag: Springer Singapore

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Abstract

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.

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Titel: Real Radicals and Finite Convergence of Polynomial Optimization Problems
verfasst von: Yoshiyuki Sekiguchi
Verlag: Springer Singapore
Buch: Advances in Mathematical Economics Volume 20
Print ISBN: 978-981-10-0475-9

Electronic ISBN: 978-981-10-0476-6

Copyright-Jahr: 2016
DOI: https://doi.org/10.1007/978-981-10-0476-6_4