Constraint Evaluates as False Logical

[C. Priess]

I have a constraint that evaluates as a false logical, and am unable to determine the reason.  A toy version of the code that reproduces the problem is below:

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N=25;
x0=0.1*randn(N,1);

opt=sdpsettings('usex0',1);

P=randn(N,N);
P=P'*P;

a=0.9;  

x=sdpvar(N,1);
assign(x,x0);  

obj=sum(P*x);

c0=zeros(N,1);
r0=zeros(1,N);
r=r0;

Acl=zeros(N,1);

for i=2:N
   r(i)=1;

   Q=1/N*toeplitz(c0,r);

   Acl(i)=x0'*Q*x0+x0'*(Q+Q')*(x-x0);

   r=r0;
end

con=[-a<=Acl<=a,-1<=x<=1];

sol=solvesdp(con,obj,opt);

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The strange-looking term "Acl" is just a local linear Taylor-series approximation of the autocorrelation function.  What is very strange is that this constraint causes Yalmip to give the error "One of the constraints evaluates to a FALSE LOGICAL variable" when a<1, but it works fine when a>=1.  However, evaluating Acl at x=x0, or indeed essentially any x within the region -1<=x<=1 produces max values of Acl which are MUCH smaller than 1.  Is this a problem because Q is, in general, singular, or is something else going on?  Thanks for any help.

[Johan Löfberg]

You have been hit by this "design feature" in MATLAB

http://users.isy.liu.se/johanl/yalmip/pmwiki.php?n=Extra.NANInModel

Hence, define Acl using concatenation instead.

[Qifeng Li]

Hi there,

So, in the end, how did you define Acl using concatenation in the for-loop?

Thanks.

[Johan Löfberg]

Acl = 0;

for i=2:N
   r(i)=1;
   Q=1/N*toeplitz(c0,r);

   Acl=[Acl x0'*Q*x0+x0'*(Q+Q')*(x-x0)];
   r=r0;
end