How to model this problem in cvx

Nonconvex
1

keeping T constant we have to minimize Q. How to code.
c1,c2 matrices NxN
X matrix Lx1 here L=4 . A order NxL a1 order 1xN

cvx_begin
variable x(4)
variable k
T=a1*c1*A*x;
Q=a1*c2*A*x;
minimize((Q))
subject to
 T is constant 
x(1)==k;
x(2)==0;
x(4)==0;
sum(x(1:3))==0.5*k;

A*x>0;
cvx_end

T is constant giving error.

2

I’m not sure why you would even think that T is constant is a valid construction in CVX. It is nowhere to be seen in the documentation. Please read that before going any further. While you are there, make sure to read this section so you aren’t surprised by what CVX does with your A*x>0 cosntraint.

But I am afraid I do not understand what you are even trying to do with T is constant. Can you describe what you want it to do?

3

I want to maximize the ratio T/Q.

4

After getting the variable vector I want to scale it to make sum®=sqrt(2).
Again spectral factorization to get prototype filter of wavelet filter bank.

5

Your model is not convex. It is, however, quasiconvex. See the section on “linear fractional programming” in Boyd & Vandenberghe’s book “Convex Optimization” to learn how to solve such problems.