Why some constraints violated?

1

I am solving a semidefinite programming (see the following code). I have checked it is feasible (I can find a simple feasible solution). However when I solve this problem with mosek and achieve an opt solution, i find this solution violates some constraints, can anybody tell me why this happens?? Thank you.
%%-----------------Matlab Code-------------------------------------------------------------------------------
cvx_begin
variable X(n+1,n+1) symmetric

minimize (trace(A0*X)+t0*k0);

subject to
   for i=1:260
       trace(A(:,:,i)*X) <= c(i);
   end
   for i=261:403
       trace(A(:,:,i)*X)==c(i);
   end
   X==semidefinite(n+1);
   diag(X)==ones(n+1,1);

cvx_end

2

Constraints will never be satisfied exactly since computations are done using finite precision floating numbers. Let us say the true solution is pi, then how will you store that in 64 bits which is the size of a floating number on a computer?

Since I cannot see the log information which has the Mosek solution summary

https://docs.mosek.com/9.2/toolbox/debugging-log.html?highlight=solution%20summary#solution-summary

then I cannot say whether the violations is bigger than one should be reasonable expected.

3

We don’t know how big the violations are so https://docs.mosek.com/9.2/faq/faq.html#why-does-the-solution-slightly-violate-constraints might be one possible answer.