Description

This repo is a fork of https://github.com/anirudhamajumdar/spotless. We added the support of power cone optimization with Mosek (https://www.mosek.com/) for paper A new characterization of symmetric H^+-tensors and M-tensors.

Installation instructions

1. git clone the repo with

https://github.com/XinEDprob/spotless.git

2. intall the spotless tool with spot_install.m
3. install Tensor Toolbox for MATLAB v3.1 for MATLAB from https://www.tensortoolbox.org/index.html
4. download allcomb(varargin) from Matlab file exchange: https://www.mathworks.com/matlabcentral/fileexchange/10064-allcomb-varargin. Unzip the downloaded file and put the unzipped in folder spotless.
5. install Mosek 9.3 from https://www.mosek.com
6. (optional) if you want to compare our methods with the one proposed in TenEig (https://epubs.siam.org/doi/abs/10.1137/15M1010725), you also need to download and install TenEig from https://users.math.msu.edu/users/chenlipi/teneig.html

Running experiments

The implementation of our methods for Table 1-3 and Example 4-7 are contained in tensor_paper/experiments.m

For implementation of Example 8

• tensor_paper/Fan_product_M_tensors.m is for the computation of H-eigenvalues with our methods.
• lb_H_eigenvalue_Fan_Prodcut.m is to compute the lower bound with the H-eigenvalues from tensor_paper/Fan_product_M_tensors.m.
• other_method_H_eigen_M_tensor.m is for the computation of H-eigenvalues with other methods in the comparison.
• other_method_H_eigen_Fan.m is to compute the lower bound with the H-eigenvalues from other_method_H_eigen_M_tensor.m

The experiments with TenEig (https://users.math.msu.edu/users/chenlipi/teneig.html) (for part of Table 2) are contained in tensor_paper/homotopy_H_eig.m