title: programming a nonconvex optimization (quadratic maximization) semidefinite programming
body: <p>just wonder if anyone could help me to solve a problem that goes like this: (with matlab and CVX)</p>
  
  <pre><code>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&lt;=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&gt;=0
  
  maximize(x1^2+x2^2+x3^2)
  
  cvx_end
  </code></pre>
  
  <p>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 fulfill as well all the other equalities/inequalities after the variable statement.</p>
  
  <p><strong>well, this program didn't work as quadratic maximization is not convex as required by CVX, someone knows of a way in which this optimization can be reformulated or solved with another resource</strong></p>
  
  <p>well, any input is acknowledge,</p>