Dear all,

I have a numerical issue when I use CVX (by SeDuMi and SDPT3) to solve an SDP problem of the form

$$\begin{array}{rl}\displaystyle\max_{{x_{nk},~y_{nk}}*{n,k}}&\displaystyle\sum_n\sum_k y*{nk}\{\rm s.t.~}&\displaystyle f(x_{nk})-y_{nk}{\bf I}*N\succeq{\bf 0},\&\displaystyle y*{nk}\geq 0,\end{array}$$

where f(x_{nk}):{\mathbb R}\mapsto\mathbb{S}^N_+ is a linear function of x_{nk} for all n and k.

If I scale the optimization variable y_{nk} by a proper scaling factor, say, \alpha=10, or 100, the linear SDP problem can be solved by CVX with `cvx_status`

= `Solved`

. But, usually, if I fixed \alpha=1 due to the difficulty of the choice of \alpha, the `CVX`

will return the result with `Inaccurate/Solved`

.

So, how can I improve the numerical stability of such kind of problems?

Thank you very much.