5 citations · 9 across the 12 of their papers we have counts for
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Some applications of Scherer-Hol's theorem for polynomial matrices
Trung Hoa Dinh, Minh Toan Ho, Cong Trinh Le
In this paper we establish some applications of the Scherer-Hol's theorem for polynomial matrices. Firstly, we give a representation for polynomial matrices positive definite on su…
A note on optimization with Morse polynomials
Công-Trình Lê
In this paper we prove that the gradient ideal of a Morse polynomial is radical. This gives a generic class of polynomials whose gradient ideals are radical. As a consequence we re…
On tangent cones at infinity of algebraic varieties
Công-Trình Lê, Tien-Son Pham
In this paper, we establish the following version at infinity of Whitney's theorem [6, 7]: Geometric and algebraic tangent cones at infinity of complex algebraic varieties coincide…
Handelman's Positivstellensatz for polynomial matrices positive definite on polyhedra
Công-Trình Lê, Thi-Hoa-Binh Du
In this paper we give a matrix version of Handelman's Positivstellensatz [1], representing polynomial matrices which are positive definite on convex, compact polyhedra. Moreover, w…
Equinormalizability and topologically triviality of deformations of isolated curve singularities over smooth base spaces
Công-Trình Lê
We give a -constant criterion for equinormalizability of deformations of isolated (not necessarily reduced) curve singularities over smooth base spaces of dimension . Fo…
Nonnegative Morse polynomial functions and polynomial optimization
Công-Trình Lê
In this paper we study the representation of Morse polynomial functions which are nonnegative on a compact basic closed semi-algebraic set in , and having only finitel…