Hi, guys. I have been working on a second-order convex problem (SOCP) using CVX, which consists of several second-order convex constraints.

Here is my problem. When the variable, for example, w_i, is in the right side, the convex problem can be solved well. For example, when the second-order constraint is like: I_k\geq \sum_{i=1}^K|h_k^Hw_i|^2+\sigma_k^2, the convex problem can be solved. Here, h_k and \sigma_k are given, and I_k is an auxiliary variable.

But when I try to solve another SOCP problem where the second-order constraint is like: e_k\geq \sum_{i=1}^K|\Theta J_kw_i|^2+\sigma_k^2 (Here \Theta is a variable and J_k and w_i are given. e_k is an auxiliary variable.), the status of the problem is still ‘Solved’, however, the second-order constraint itself is not satisfied. When I validate the results of |\Theta J_k|^2, it turns out that some entries of the matrix |\Theta J_kw_i|^2 are **negative** and some entries are quite large which is incorrect. Because J_k is around 10e-6 and w_i is around 0.01 and also \Theta should satisfy |\Theta|\leq1.

So I was wondering if CVX itself cannot solve the convex problem where the variable is in the right side?

Thank you in advance!