Equality constraint does not hold

[behrooz]

Dear friends,
I have a weird problem. I have a simple flow conservation constraint in the VNE problem:

I wrote the code in CVX, and for some cases it must be infeasible. But CVX solved it!
As you can see in the below code, lines 32-40 for i=3 and j=2, the right-hand
side of the equality constraint is equal to 8 but the left-hand side is equal
to 0!. So, CVX must report it’s infeasible.

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clear all;
cvx_clear;
%cvx_solver mosek;

s_nodes=4;
v_nodes=3;

s_net_topology=[0,0,1,1;1,0,1,0;0,0,0,0;1,0,0,0];
s_link_capacity=[0,0,79,73;92,0,48,0;0,0,0,0;47,0,0,0];
[row_s,col_s]=find((s_net_topology)~=0);

v_net_topology=[0,0,1;1,0,0;0,0,0];
v_link_capacity=[0,0,8;2,0,0;0,0,0];
[row_v,col_v]=find((v_net_topology)~=0);
%%% 
x=zeros(v_nodes,s_nodes);
x(3,1)=1;
x(2,2)=1;
x(1,3)=1;

%%
cvx_begin
    
   variable y(v_nodes,v_nodes,s_nodes,s_nodes) nonnegative;

    
   minimize 1000*sum(sum(sum(sum(y(:,:,:,:)))))+1000*sum(sum(x(:,:)));
   
   subject to
    
   for i=1:s_nodes
    for j=1:sum(nonzeros(v_net_topology))%# of virtual links
        [ph1]=find(s_net_topology(i,:)~=0);
        [ph2]=find(s_net_topology(:,i)~=0);
        %test with j=2 i=3 : row_v=2 col_v=1 => 0==8 !!!!
        sum(y(row_v(j),col_v(j),i,ph1(:)))-sum(y(row_v(j),col_v(j),ph2(:),i)) == v_link_capacity(row_v(j),col_v(j))*(x(row_v(j),i)-x(col_v(j),i));

    end
   end
   
  
   for i=1:sum(nonzeros(s_net_topology))
      
       arrind=null(1,4);
       for j=1:sum(nonzeros(v_net_topology))
           a=[row_v(j),col_v(j),row_s(i),col_s(i)];
           arrind=vertcat(arrind,a);
       end
       sum(y(arrind(:)))<=s_link_capacity(row_s(i),col_s(i));

       
   end
   
cvx_end

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