How to solve optimization problem with non-convex equality constraint and LMIs?

[Parikshit Pareek]

I have a problem which has a non-convex equality constraint. The constraints are quadratic/ bilinear in nature. Along with these, I have an LMI constraint as well. 

I tried solving them using BMIBNB but it gives an error of no suitable solver. It solves the non-convex problem and LMI individually but not together. 

Can I solve them together using YALMIP?

if yes then,

Which solver combination I should be using?

PS: I am aware of the limitations of a global solver. Yet I am looking for a feasible solution with a finite optimality gap.  

[Johan Löfberg]

final example

https://yalmip.github.io/tutorial/globaloptimization/

[Johan Löfberg]

or if the LMI H>= 0 is of small dimension, introduce new matrix R (sufficient with triangular parameterization) and add constraint R*R' = H. That way you can remove the LMI, and hope that the quadratic equalities are sufficiently few and simple, and thus arrive at a nonconvex quadratic problem