I am using CVX to solve an optimization problem. One of my constraints in the problem is
$$M \succeq \eta {\eta}^T$$
where $M$ is a square matrix and $\eta$ is a column vector (both $M$ and $\eta$ are variables). CVX issues the error
Only scalar quadratic forms can be specified in CVX.
I think the error results from the quadratic form of the constraint. I am wondering whether I can convert the constraint into another equivalent form?
(Update) Here is the optimization problem I am trying to solve:
$$ \begin{align} \label{svm_new_obj_semi} & {\min}_{\boldsymbol{\eta}, M, \boldsymbol{\nu}, \boldsymbol{w}, \delta} \,\,\delta \\ \text{s.t.} & \quad \boldsymbol{\nu} \succeq 0 \nonumber \\ & \quad \boldsymbol{w} \succeq 0 \nonumber \\ & \quad 0 \preceq \boldsymbol{\eta} \preceq 1, \nonumber \\ & \quad M \succeq \boldsymbol{\eta} {\boldsymbol{\eta}}^T \nonumber \\ & \quad \begin{bmatrix} G\circ M & \boldsymbol{\eta} + \boldsymbol{\nu} - \boldsymbol{w} \\ {(\boldsymbol{\eta} + \boldsymbol{\nu} - \boldsymbol{w} )}^T & \frac{2}{\beta}( \delta - {\boldsymbol{w}}^T\boldsymbol{e} + {\boldsymbol{\eta}}^T \boldsymbol{e} ) \end{bmatrix} \succeq 0 \end{align} $$
I am trying to use: $0 \preceq M \preceq \boldsymbol{A}$, $diag(M) \preceq \boldsymbol{\eta}$, where $\boldsymbol{A}$ is a all ones matrix, to approximate $M \succeq \boldsymbol{\eta} {\boldsymbol{\eta}}^T$. Is this reasonable?
