YALMIP outputs "Infeasible" for an easy, feasible SDP - matlab

Question

I want to determine whether a given 3x3 matrix is positive-semidefinite or not. To do so, I write the following SDP in YALMIP
v=0.2;
a=sdpvar(1);
b=sdpvar(1);
M=[1 a -v/4 ; b 1 0 ; -v/4 0 0.25];
x=sdpvar(1);
optimize([M+x*eye(3)>=0],x,sdpsettings('solver','sedumi'))
This program gives me the error "Dual infeasible, primal improving direction found". This happens for any value of v in the interval (0,1].
Given that this problem is tractable, I diagonalized the matrix directly obtaining that the three eigenvalues are the three roots of the following polynomial
16*t^3 - 36*t^2 + (24 - 16*a*b - v^2)*t + (-4 + 4*a*b + v^2)
Computing the values of the three roots numerically I see that the three of them are positive for sign(a)=sign(b) (except for a small region in the neighborhood of a,b=+-1), for any value of v. Therefore, the SDP should run without problems and output a negative value of x without further complications.
To make things more interesting, I ran the same code with the following matrix
M=[1 a v/4 ; b 1 0 ; v/4 0 0.25];
This matrix has the same eigenvalues as the previous one, and in this case the program runs without any issues, confirming that the matrix is indeed positive-semidefinite.
I am really curious about the nature of this issue, any help would be really appreciated.
EDIT: I also tried the SDPT3 solver, and results are very similar. In fact, the program runs smoothly for the case of +v, but when i put a minus sign I get the following error
'Unknown problem in solver (Turn on 'debug' in sdpsettings) (Error using & …'
Furthermore, when I add some restrictions to the variables, i.e., I run the following command
optimize([total+w*eye(3)>=0,-1<=a<=1,-1<=b<=1],w,sdpsettings('solver','sdpt3'))
Then the error turns to an 'Infeasible problem' error.

Answer 1

Late answer, but anyway. The matrix you have specified is not symmetric. Semidefinite programming is about optimization over the set of symmetric positive semi-definite matrices.
When you define this unsymmetric matrix constraint in YALMIP, it is simply interpreted as a set of 9 linear elementwise constraints, and for that linear program, the optimal x is unbounded.