I want to solve this problem:
min_phi phi’*Gamma*phi  2*real(gamma’*phi)
s.t. norm( 2*phiones(N,1) , Inf ) <= 1;
Xi*phi == ones(M,1);
phi’*Q*phi <= power;
where phi is a vector of N \times 1, Gamma and Q are positive semidefinite, Gamma is singular, and Q is of fullrank.
The problems are listed as follows:

I have transformed the objective function and the power constraint into norm form:
minimize ( norm( sqrt_Gamma*phi  new_gamma ) )
and
norm( sqrt_Q*phi ) <= sqrt(power)
However, I still wonder if there’s any other better way to recast a quadratic function? 
As mentioned before, Gamma is not a fullrank matrix. When I transform the objective function into the norm form, I have to calculate inv(Gamma^(1/2)). Is there a way to avoid the inverse operation?

I am currently using Mosek, does Mosek fit this kind of problem?