All Questions

Hello! (First question--please forgive me if its unclear.) I am interested in efficient/approximate optimization techniques for minimizing a norm of a convex combination of symmetric, positive semi-...

The cone of symmetric positive semidefinite $n\times n$ matrices is the convex hull of rank $1$ matrices. That is, every symmetric positive semidefinite matrix is a convex combination of rank 1 ...

Let $S_+$ be the cone of psd matrices ($n\times n$ real symmetric positive semidefinite matrices). This cone is a metric space induced from the inner product $\langle A,B\rangle = tr (AB)=tr(BA)$. ...

I would like to state that this is related to a past question of mine which contained errors and now appears in the corrected form, with the erroneous one deleted and closed. In my research of linear ...

Let $\mathbf{A}$ and $\mathbf{B}$ be two complex rank-one $N\times N$ positive semi-definite matrices. Let the matrix $\mathbf{C}$ be defined as \begin{align} \mathbf{C}=\left(\mathbf{I}*\frac{1}{\...

Suppose you have a concave function defined over a non-polyhedral convex cone and you are interested in the infimum. What would be standard approaches to tackle the question? (The cone is actually PSD ...