54 citations · 155 across the 71 of their papers we have counts for
5 papers · 1 filter
The Algebraic Degree of Semidefinite Programming
Jiawang Nie, Kristian Ranestad, Bernd Sturmfels
Given a generic semidefinite program, specified by matrices with rational entries, each coordinate of its optimal solution is an algebraic number. We study the degree of the minima…
An elementary and constructive solution to Hilbert's 17th Problem for matrices
Christopher J. Hillar, Jiawang Nie
We give a short and elementary proof of a theorem of Procesi, Schacher and (independently) Gondard, Ribenboim that generalizes a famous result of Artin. Let be an …
Sparse SOS Relaxations for Minimizing Functions that are Summations of Small Polynomials
Jiawang Nie, James Demmel
This paper discusses how to find the global minimum of functions that are summations of small polynomials (``small'' means involving a small number of variables). Some sparse sum o…
Sum of Squares Method for Sensor Network Localization
Jiawang Nie
This paper has been withdrawn by the author due to its publication
Global Minimization of Rational Functions and the Nearest GCDs
Jiawang Nie, James Demmel, Ming Gu
This paper has been withdrawn by the authors due to its publication