I am trying to solve, the following optimization problem using CVX

min_X \lambda_{max}(X)

subject to

a_i'Xa_j = 0; for\, i = 1......n;

X>=0;

where A is a matrix of order m \times n with m>n and X is of size m \times m.

when I am running this problem of order, say, 4096 \times 4000, I am getting error “out of memory”.

The default solver I am using in CVX is SDPT3. I tried with other solvers too like SeDuMi and MoSek etc.

CVX can solver largescale problems? what kind of solver I need to use and what are system configurations need to solve fast.

Thank you so much for your time.