s.t. 5sqrt((x-5)^2+(y-5)^2+10)+10<=U(n);
as is show above in the left of this founction should be convex ，U(n) is slack variable, x,y is variable
as we all know sqrt(convex )is illegal can we use another slack varaible to express (x-5)^2+(y-5)^2+10,as below:
W_fea=(xi-5)^2+(yi-5)^2+10
variable: W(n) U(n)
W(n)>= (x-5)^2+(y-5)^2+10
5sqrt(W_fea(n))/2+W(n)/(2*sqrt(W_fea(n)))+10<=U(n);
How to express sqrt((x-5)^2+(y-5)^2+10)
sqrt((x-5)^2+(y-5)^2+10) = norm([x-5;y-5;sqrt(10)] =|| Ax+b ||
for a suitable A and b. That will work.
after three minutes posted this question on the forum ,i tried this way ,that’s really work .thanks