How can a semidefinite positive program can be done?

just wonder if anyone could help me to solve a problem that goes like this: (with matlab and CVX)

cvx_begin sdp

variables x0 x1 x2 x3 y1 y2 y3 y4 y5

x0==1/sqrt(3)

1/3+x1^2+x2^2+x3^2+y1^2+y2^2+y3^2+y4^2+y5^2<=1

x1==-x3 
y1==y5
y2==-y4 

x0*X0+x1*X1+x2*X2+x3*X3+y1*Y1+y2*Y2+y3*Y3+y4*Y4+y5*Y5>=0

maximize(x1^2+x2^2+x3^2)

cvx_end

X0, X1,.....X3,Y1,....Y5,Z1.......Z7 (in capital letters) are matrices (spherical tensors) One constraint is that the product with the variables in lowercase must be positive semidefinite, also it has to fulfil as well all the other equalities/inequalities after the variable statement.

well, this program didn't work as quadratic maximization is a not convex as required by cvx, someone knows of a way in which this optimization can be reformulated or solved with another resource

well, any input is acknowledge,

thanks, Pablo