Look at How to handle nonlinear equality constraints? , http://stanford.edu/class/ee364b/lectures/seq_slides.pdf , http://stanford.edu/~boyd/papers/cvx_ccv.html .
Are your E(:,:,k) all psd? If psd, at least now your problem will have been stated in a somewhat more understandable fashion than originally, so maybe someone can come along to provide you more specific guidance or direct you to a more appropriate forum if you still need it.