Necessary and sufficient conditions for S-lemma and nonconvex quadratic optimization
| العنوان: | Necessary and sufficient conditions for S-lemma and nonconvex quadratic optimization |
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| المؤلفون: | Guoyin Li, N. Q. Huy, Vaithilingam Jeyakumar |
| المصدر: | Optimization and Engineering. 10:491-503 |
| بيانات النشر: | Springer Science and Business Media LLC, 2008. |
| سنة النشر: | 2008 |
| مصطلحات موضوعية: | Lemma (mathematics), Control and Optimization, Mechanical Engineering, Aerospace Engineering, Quadratic function, Slater's condition, Convexity, Combinatorics, Constraint (information theory), Quadratic equation, Applied mathematics, Quadratic programming, Electrical and Electronic Engineering, Link (knot theory), Software, Civil and Structural Engineering, Mathematics |
| الوصف: | The celebrated S-lemma establishes a powerful equivalent condition for the nonnegativity of a quadratic function over a single quadratic inequality. However, this lemma fails without the technical condition, known as the Slater condition. In this paper, we first show that the Slater condition is indeed necessary for the S-lemma and then establishes a regularized form of the S-lemma in the absence of the Slater condition. Consequently, we present characterizations of global optimality and the Lagrangian duality for quadratic optimization problems with a single quadratic constraint. Our method of proof makes use of Brickman’s theorem and conjugate analysis, exploiting the hidden link between the convexity and the S-lemma. |
| تدمد: | 1573-2924 1389-4420 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_________::4dd3e075d93516de101497d0796d2321 https://doi.org/10.1007/s11081-008-9076-9 |
| حقوق: | OPEN |
| رقم الأكسشن: | edsair.doi...........4dd3e075d93516de101497d0796d2321 |
| قاعدة البيانات: | OpenAIRE |
Find this article in full text from Springer Verlag. | تدمد: | 15732924 13894420 |
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