An optimization probelm contatining a slightly concave constraint

[wang lingyi]

Hello,

I am trying to solve the following optimization problem, and the equality constraint is slightly concave, since the eigenvalue of Hessian matrix B_i  is slightly negative, as attached below. I want to ask, if there is any computationally efficient way to solve the following problem? And if mosek can solve it, how many seconds will the solver spend? Hope you can reply me. Thank you so much. 

[Erling D. Andersen]

Even if B_i is positive sem-definite, then your problem is not convex at all since you have a nonlinear equality.

E.g.

x^2 = 1

does not define a convex set.

[wang lingyi]

Dear Andersen,
Thank you for replying me. Do you have any suggestion of solving it in a computationally efficient way? Hope you can reply me. Thank you so much.

Sincerely,

[Erling D. Andersen]

No.