Polynomial optimization with real varieties (Q2866200)

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.