Constraints not satisfied even though problem successfully solved

[Hossein Ghafarian]

Dear Dr Johan,

I write the following problem using YALMIP(mosek) and the solver reports it is solved and it is near optimal. But some of the constraints not satisfied. A minimal problem is 

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initL=[1,2];

n=4;

c=10;

n_l=2;

n_u=2;

n_Vt=2;

nap=6;

dSize=1;

V     =sdpvar(nap+1,nap+1);

Vt=sdpvar(n_u,1);

r=sdpvar(n_u,1);

beta_p=sdpvar(nap,1);

eta_p =sdpvar(nap,1);

t     =sdpvar(1,1);

setall   =1:n;

setunlab =setdiff(setall,initL);

setVtuery =n+1:nap;

y_l     =[-1;1];

KVMatrix     = sdpvar(nap+1,nap+1);

s=sdpvar(nap,1);

KVt= [1     ,0.5794,0.7166,0.8211,0.7166,0.8211;...

     0.5794,1     ,0.8084,0.7057,0.8084,0.7057;...

     0.7166,0.8084,1     ,0.8727,1     ,0.8727;...

     0.8211,0.7057,0.8727,1     ,0.8727,1     ;...

     0.7166,0.8084,1     ,0.8727,1     ,0.872 ;...

     0.8211,0.7057,0.8727,1     ,0.8727,1     ];

 KVt=(KVt+KVt')/2;%force symmetry

KVMatrix = [KVt.*V(1:nap,1:nap) ,1-s+eta_p-beta_p;(1-s+eta_p-beta_p)',2*t];

cObjective = t+sum(beta_p)+sum(eta_p(n+1:nap))+c*sum(r);

cConstraint=[beta_p>=0,eta_p>=0,V>=0,KVMatrix>=0];

cConstriant=[cConstraint,sum(Vt)==dSize,0<=Vt,Vt<=1];

cConstraint=[cConstraint,V(nap+1,nap+1)==1,diag(V(1:nap,1:nap))<=1,V(initL,nap+1)==y_l];

cConstraint=[cConstraint,r>=V(n_l+1:n,nap+1),r>=-V(n_l+1:n,nap+1),r+Vt==1];

cConstraint=[cConstraint,V(n+1:nap,nap+1)==Vt,s==zeros(nap,1),s(setunlab)==Vt];

sol = optimize(cConstraint,cObjective);

if sol.problem==0

    info.primal=true;

    info.Vprimal     = value(V);

    info.primalVt     = value(Vt);

    beta_pr  = value(beta_p);

    eta_pr   = value(eta_p);

    info.r=value(r);

    info.s=value(s);

end

sum(value(Vt))==dSize % this constraint is not satisfied.

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I don't know why, and what I have to do in order to make it correct. I checked constraints using checkset, it has a slight infeasibility,-1e^-9. 

Thank you very much. 

[Johan Löfberg]

See any difference on the left-hand side?

[Hossein Ghafarian]

Dear Johan, 

Thank you very much. you are excellent.