sdpvar x y n
sdpvar pc0 pc1 pc2 pc3 pc4 pc5 pc6 pc7 pc8 pc9
sdpvar v1 v2
sdpvar u1 u2 u3 u4 u5 u6 u7
FeasibilityConstraints=[sos(pc0+pc1*(x)+pc2*(y)+pc3*(n)+pc4*(x)*(x)+pc5*(x)*(y)+pc6*(x)*(n)+pc7*(y)*(y)+pc8*(y)*(n)+pc9*(n)*(n)-(x+0.25*n*y)+v1*(x-0)-u1*(y-0)+v2*(x-0)*(y-0)),...
sos(x-(pc0+pc1*(x)+pc2*(y)+pc3*(n)+pc4*(x)*(x)+pc5*(x)*(y)+pc6*(x)*(n)+pc7*(y)*(y)+pc8*(y)*(n)+pc9*(n)*(n))-u2*(0-n)-u3*(y-0)-u4*(0-n)*(y-0)),...
sos(0.25*(pc0+pc1*(x+y)+pc2*(y)+pc3*(n-1)+pc4*(x+y)*(x+y)+pc5*(x+y)*(y)+pc6*(x+y)*(n-1)+pc7*(y)*(y)+pc8*(y)*(n-1)+pc9*(n-1)*(n-1))+ (1-0.25)*(pc0+pc1*(x)+pc2*(y)+pc3*(n-1)+pc4*(x)*(x)+pc5*(x)*(y)+pc6*(x)*(n-1)+pc7*(y)*(y)+pc8*(y)*(n-1)+pc9*(n-1)*(n-1))-(pc0+pc1*(x)+pc2*(y)+pc3*(n-1)+pc4*(x)*(x)+pc5*(x)*(y)+pc6*(x)*(n-1)+pc7*(y)*(y)+pc8*(y)*(n-1)+pc9*(n-1)*(n-1))-u5*(n-0)-u6*(y-0)-u7*(n-0)*(y-0)),...
u1>=0, u2>=0, u3>=0, u4>=0, u5>=0, u6>=0, u7>=0];
options=sdpsettings('verbose',1,'solver','sedumi');
solvesos(FeasibilityConstraints,[ ],options,[pc0;pc1;pc2;pc3;pc4;pc5;pc6;pc7;pc8;pc9;v1;v2;u1;u2;u3;u4;u5;u6;u7]) 
 vpc0=value(pc0)  
 vpc1=value(pc1)  
 vpc2=value(pc2)  
 vpc3=value(pc3)  
 vpc4=value(pc4)  
 vpc5=value(pc5)  
 vpc6=value(pc6)  
 vpc7=value(pc7)  
 vpc8=value(pc8)  
 vpc9=value(pc9) 