How to express sqrt((x-5)^2+(y-5)^2+10)

1

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);

2

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.

3

after three minutes posted this question on the forum ,i tried this way ,that’s really work .thanks

4

thanks for your advice