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math.OC2010★ 3 cited
An Exact Jacobian SDP Relaxation for Polynomial Optimization
Jiawang Nie
Given polynomials f(x), g_i(x), h_j(x), we study how to minimize f on the semialgebraic set S = { x \in R^n: h_1(x)=...=h_{m_1}(x) =0, g_1(x) >= 0, ..., g_{m_2}(x) >= 0}. Let f_{mi…
math.OC2010★ 3 cited
Discriminants and Nonnegative Polynomials
Jiawang Nie
For a semialgebraic set K in R^n, let P_d(K) be the cone of polynomials in R^n of degrees at most d that are nonnegative on K. This paper studies the geometry of its boundary. When…