What is the internal principle of CVX when minimizing a function like following?

1

variable T(Lu,Lu) hermitian toeplitz semidefinite;
minimize( norm(GTG’-Rxx,‘fro’) + mu * norm_nuc(T) );

where G and Rxx are known.
I want to learn the principle like algorithm or function.
Thank you!

2

The answer depends on which optimizer cvx is using.

For instance if you use SeDuMi see

@article{doi:10.1080/10556789908805766,
  author = {Sturm, Jos F.},
  title = {Using SeDuMi 1.02, A {MATLAB} toolbox for optimization over symmetric cones},
  journal = {Optimization Methods and Software},
  volume = {11},
  number = {1-4},
  pages = {625-653},
  year  = {1999},
  doi = {10.1080/10556789908805766},
  URL = {https://doi.org/10.1080/10556789908805766}
}
3

I use sdpt3 as optimizer， I don’t know how the optimizer can achieve the optimization goal? So I really want to know the internal algorithm.

4

May I suggest you try to Google

SDPT3

Maybe something useful shows up.

5

OK，thank you for your help！