54 citations · 155 across the 71 of their papers we have counts for
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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…
Semidefinite Relaxations for Best Rank-1 Tensor Approximations
Jiawang Nie, Li Wang
This paper studies the problem of finding best rank-1 approximations for both symmetric and nonsymmetric tensors. For symmetric tensors, this is equivalent to optimizing homogeneou…
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…
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…