5 papers
A Tight SDP Relaxation for the Cubic-Quartic Regularization Problem
Jinling Zhou, Xin Liu, Jiawang Nie +1
This paper studies how to compute global minimizers of the cubic-quartic regularization (CQR) problem \[ \min_{s \in \mathbb{R}^n} \quad f_0+g^Ts+\frac{1}{2}s^THs+\fracβ{6}\| s \|^…
Robust Completion for Rank-1 Tensors with Noises
Jiawang Nie, Xindong Tang, Jinling Zhou
This paper studies the rank-1 tensor completion problem for cubic tensors when there are noises for observed tensor entries. First, we propose a robust biquadratic optimization mod…
The Rank-1 Completion Problem for Cubic Tensors
Jinling Zhou, Jiawang Nie, Zheng Peng +1
This paper studies the rank- tensor completion problem for cubic tensors. First of all, we show that this problem is equivalent to a special rank- matrix recovery problem. Wh…
Diagonal Gaussian Mixture Models and Higher Order Tensor Decompositions
Bingni Guo, Jiawang Nie, Zi Yang
This paper studies how to recover parameters in diagonal Gaussian mixture models using tensors. High-order moments of the Gaussian mixture model are estimated from samples. They fo…
Local Versus Global Conditions in Polynomial Optimization
Jiawang Nie
This paper reviews local and global optimality conditions in polynomial optimization. We summarize the relationship between them.