Hi there,
I’m trying to solve the following optimization problem:
where 
and 
are both n-by-1 vectors, I wrote in matlab the following:
cvx_begin
variable X(2*n,1) nonnegative
minimize [ones(1,n), zeros(1,n)] * X;
subject to
log(1 + c * pow_p([eye(n),zeros(n)]*X,-2)) + log(1+power(1/4,[zeros(n),eye(n)]*X)) <= d;
[zeros(1,n),ones(1,n)] * X <= R;
cvx_end
I’ve managed to write 
and 
according to DCP rules using 
and 
respectively, but there’s still the problem of log{ (convex) } of the first term in the first constraint function. But 
is indeed convex.
So my question is how to rewrite the first constraint function that obeys the DCP rules?
Thank you.