An effective version of Schmüdgen’s Positivstellensatz for the hypercube
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Springer
2023
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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 |
8.893527 |