How to find projection on a set

Let us define . We have

g1=(x1-100)*(x1-150)<=0;

g2=(x2-100)*(x2-150)<=0;

g3=(x3-100)*(x3-200)<=0; I want to find . Please help me find the projection fun P as defined. I tried this code but it gives error.

syms x1 x2 x3 g1 g2 g3 t

g1=(x1-100)*(x1-200)<=0;
g2=(x2-100)*(x2-200)<=0;
g3=(x3-100)*(x3-200)<=0;

% g1,g2,g3 has set of values of x1, x2, x3. 
[difference, index_At_F_Equals_x1] = argmin(abs(g1-x1))
% Value of projection fun
P1 = g1(index_At_F_Equals_x1)

[difference, index_At_F_Equals_x2] = argmin(abs(g2-x2))
P2 = g2(index_At_F_Equals_x2)

[difference, index_At_F_Equals_x3] = argmin(abs(g3-x3))
P3 = g3(index_At_F_Equals_x3)

Answer 1

[Matt J]

The set appears just to be a box, so,

lb=[100;100;100];
ub=[150;150;200];

P= @(x) min( max(x(:),lb) ub);