I want to solve this problem:
min_phi phi’*Gamma*phi - 2*real(gamma’*phi)
s.t. norm( 2*phi-ones(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 semi-definite, Gamma is singular, and Q is of full-rank.
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 ) )
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 full-rank 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?