54 citations · 155 across the 71 of their papers we have counts for
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math.OC2013★ 1 cited
The Hierarchy of Local Minimums in Polynomial Optimization
Jiawang Nie
This paper studies the hierarchy of local minimums of a polynomial in the space. For this purpose, we first compute H-minimums, for which the first and second order optimality cond…
math.OC2013
Free Semidefinite Representation of Matrix Power Functions
J. William Helton, Jiawang Nie, Jeremy S. Semko
Consider the matrix power function X^p defined over the cone of positive definite matrices S^{n}_{++}. It is known that X^p is convex over S^{n}_{++} if p is in [-1,0] or [1,2] and…
math.OC2013★ 3 cited
Linear Optimization with Cones of Moments and Nonnegative Polynomials
Jiawang Nie
Let A be a finite subset of N^n and R[x]_A be the space of real polynomials whose monomial powers are from A. Let K be a compact basic semialgebraic set of R^n such that R[x]_A con…