Out of memory problem

I am facing out of memory problem when solving following problem using CVX in MATLAB version 2014a in windows 10.

let A be m\times n matrix.


variable X(m,m) symmetric

min_X( max_{i\neq j} A^TXA)
subject to diag(A^TXA) = 1 for i = 1,2,....n,
X == semidefinite(m).

where A is of size 1024\times 1024 and X is of size 1024 \times 1024. When I run this problem, using CVX, Its giving out of memory problem.

Please help me. Thanks in advance.