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An effective version of Schmüdgen’s Positivstellensatz for the hypercube

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Main Authors: Monique, Laurent, Lucas, Slot
Format: Book
Language:English
Published: Springer 2023
Subjects:
S⊆Rn
expressing f+η
Online Access:https://dlib.phenikaa-uni.edu.vn/handle/PNK/7420
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spelling oai:localhost:PNK-74202023-04-03T03:27:40Z An effective version of Schmüdgen’s Positivstellensatz for the hypercube Monique, Laurent Lucas, Slot S⊆Rn expressing f+η CC BY Let S⊆Rn be a compact semialgebraic set and let f be a polynomial nonnegative on S. Schmüdgen’s Positivstellensatz then states that for any η>0, the nonnegativity of f+η on S can be certified by expressing f+η as a conic combination of products of the polynomials that occur in the inequalities defining S, where the coefficients are (globally nonnegative) sum-of-squares polynomials. It does not, however, provide explicit bounds on the degree of the polynomials required for such an expression. 2023-04-03T03:21:29Z 2023-04-03T03:21:29Z 2022 Book https://dlib.phenikaa-uni.edu.vn/handle/PNK/7420 en application/pdf Springer
institution Digital Phenikaa
collection Digital Phenikaa
language English
topic S⊆Rn
expressing f+η
spellingShingle S⊆Rn
expressing f+η
Monique, Laurent
Lucas, Slot
An effective version of Schmüdgen’s Positivstellensatz for the hypercube
description CC BY
format Book
author Monique, Laurent
Lucas, Slot
author_facet Monique, Laurent
Lucas, Slot
author_sort Monique, Laurent
title An effective version of Schmüdgen’s Positivstellensatz for the hypercube
title_short An effective version of Schmüdgen’s Positivstellensatz for the hypercube
title_full An effective version of Schmüdgen’s Positivstellensatz for the hypercube
title_fullStr An effective version of Schmüdgen’s Positivstellensatz for the hypercube
title_full_unstemmed An effective version of Schmüdgen’s Positivstellensatz for the hypercube
title_sort effective version of schmüdgen’s positivstellensatz for the hypercube
publisher Springer
publishDate 2023
url https://dlib.phenikaa-uni.edu.vn/handle/PNK/7420
_version_ 1762184302116732928
score 8.887836

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