How to update constraint in nonlinear optimization

I have a location facility project where i should optimize the cost of implementing it using fmnincon. The problem is i have a condition on (x,y) (this is th coordinate of my facilities):

sqrt((x-15)^2+(y-48)^2))>10

sqrt((x-18)^2+(y-12)^2))>10

Since this two equation are non linear i can define this function:

function [c,ceq]=NLcon(z)
ceq=[];
c(1)=-z(1)^2 +26*z(1)-z(2)^2+96*z(2)-2473+100;
c(2)=-z(1)^2+36*z(1)+24*z(2)-z(2)^2-468+100;
end

but how can I add this constraint: if 20<=y<=40 then x<=20?

Answer 1

[Matt J]

Divide into 3 sub-problems. Solve with the constraints

(1) y<=20 and NLcon

(2) 20<=x<=40, y<=20, and NLcon

(3) y>=20 and NLcon

Take the solution to whichever of the 3 sub-problems gives the most optimal cost value.

[Mohamed Hmamouch]

Thank you for your answer but i have here:

this the equation that i should optimize

and this is my constraint

if 20<=y<=40 then x<=20

and i have y>=0 (as lower bound)

y>-2*x+20 ( i can define it in A)

I'm waiting as output (x,y)

so we can't define three cases where my x can be unconstrained

[Matt J]

so we can't define three cases where my x can be unconstrained

Since you accepted the answer, I assume you figure it out?

If not, see my updated answer.