Polynomial optimization with real varieties (Q2866200)
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scientific article; zbMATH DE number 6238053
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Polynomial optimization with real varieties |
scientific article; zbMATH DE number 6238053 |
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13 December 2013
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polynomial optimization
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finite convergence
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Lasserre's hierarchy
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real variety
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semidefinite program
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sum of squares
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Polynomial optimization with real varieties (English)
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The author studies the following polynomial optimization problem NEWLINE\[NEWLINEf_{\min}: \min f(x),\qquad\text{s.t.}\quad h_i(x)= 0\;(i=1,\dots, m_1),\quad g_j(x)= 0\;(j= 1,\dots, m_2),NEWLINE\]NEWLINE where \(f\) and all \(g_j\) and \(h_i\) are real polynomials in \(x\).NEWLINENEWLINE Laserre's hierarchy is a sequence of sum of square relaxations for finding the global minimum \(f_{\min}\).NEWLINENEWLINE The author proves some open questions on the convergence of Lasserre's hierarchy.
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