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Consider the following convex optimization problem

\begin{align} \max_{\mathbf{X},\mathbf{v}}~&~\mbox{trace}(\mathbf{QX}) \\s.t.&~~\mbox{diag}(\mathbf{v})-\mathbf{X}\succeq 0 \\ &~~ \mathbf{X} \succeq 0,~~\mathbf{e}^T \mathbf{v}\,=\,1 \end{align}

where $\mathbf{Q}$ is a given symmetric $n \times n$ matrix, and vector $\mathbf{e}$ is the all-ones vector in $\mathbb{R}^n$.

Is there a way of writing this as a standard semidefinite optimization problem?. The main goal is to input this to a publicly available solver like CVX or others in a form that is more well known and thus has custom made implementation. I would less prefer the route of passing this to a generic convex optimization solver.

Rodrigo de Azevedo
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dineshdileep
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    You might already know this, but in case you’re not able to get a helpful answer here, there’s always the Computational Science SE. – Theoretical Economist Oct 15 '19 at 04:00
  • @TheoreticalEconomist thanks, I will wait for couple of days before I do that – dineshdileep Oct 15 '19 at 04:08
  • So you don't want to enter this pretty much directly as written into CVX, which you can do? If not, please clarify what you are trying to accomplish. CVX will convert what you enter into the form needed by the chosen solver. – Mark L. Stone Oct 16 '19 at 18:53
  • @MarkL.Stone when I said CVX, I meant the package CVXOPT, rather than CVXPY or CVX which supports any convex optimization problem. I realized that now. But given that, is there a way to convert this into any standard well known convex optimization problem? – dineshdileep Oct 17 '19 at 09:27
  • You can use CVXPY to call CVXOPT and not have to worry about putting the problem in "standard form". – Mark L. Stone Oct 17 '19 at 11:07
  • @MarkL.Stone Got it!. I am trying that now. But, let's just say that I need to convert it to a standard form. Is there a way? – dineshdileep Oct 18 '19 at 06:30

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