Representations of non-negative polynomials via KKT ideals
This paper studies the representation of a non-negative polynomial f on a non-compact semi-algebraic set K modulo its KKT (Karush–Kuhn–Tucker) ideal. Under the assumption that f satisfies the boundary Hessian conditions (BHC) at each zero of f in K, we show that f can be represented as a sum of squa...
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| Định dạng: | Journal article |
| Ngôn ngữ: | English |
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2023
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| Truy cập trực tuyến: | https://scholar.dlu.edu.vn/handle/123456789/2329 |
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oai:scholar.dlu.edu.vn:123456789-23292023-06-14T02:25:14Z Representations of non-negative polynomials via KKT ideals Đặng, Tuấn Hiệp This paper studies the representation of a non-negative polynomial f on a non-compact semi-algebraic set K modulo its KKT (Karush–Kuhn–Tucker) ideal. Under the assumption that f satisfies the boundary Hessian conditions (BHC) at each zero of f in K, we show that f can be represented as a sum of squares (SOS) of real polynomials modulo its KKT ideal if f ≥ 0 on K. 102 2 101-109 2023-05-19T07:04:41Z 2023-05-19T07:04:41Z 2011 Journal article Bài báo đăng trên tạp chí thuộc ISI, bao gồm book chapter https://scholar.dlu.edu.vn/handle/123456789/2329 10.4064/ap102-2-1 en Annales Polonici Mathematici |
| institution |
Thư viện Trường Đại học Đà Lạt |
| collection |
Thư viện số |
| language |
English |
| description |
This paper studies the representation of a non-negative polynomial f on a non-compact semi-algebraic set K modulo its KKT (Karush–Kuhn–Tucker) ideal. Under the assumption that f satisfies the boundary Hessian conditions (BHC) at each zero of f in K, we show that f can be represented as a sum of squares (SOS) of real polynomials modulo its KKT ideal if f ≥ 0 on K. |
| format |
Journal article |
| author |
Đặng, Tuấn Hiệp |
| spellingShingle |
Đặng, Tuấn Hiệp Representations of non-negative polynomials via KKT ideals |
| author_facet |
Đặng, Tuấn Hiệp |
| author_sort |
Đặng, Tuấn Hiệp |
| title |
Representations of non-negative polynomials via KKT ideals |
| title_short |
Representations of non-negative polynomials via KKT ideals |
| title_full |
Representations of non-negative polynomials via KKT ideals |
| title_fullStr |
Representations of non-negative polynomials via KKT ideals |
| title_full_unstemmed |
Representations of non-negative polynomials via KKT ideals |
| title_sort |
representations of non-negative polynomials via kkt ideals |
| publishDate |
2023 |
| url |
https://scholar.dlu.edu.vn/handle/123456789/2329 |
| _version_ |
1778233852052897792 |