Let’s consider the following conditional constraint. w is a set of input data. x,y(1:3),d(1:3) are the decision variables.
x= 3.9 % optimization variable (one can iterate over it 0<x<5 ) for i=1:3 if w[i]-x <=0 d[i]=x-w[i]; y[i]= w[i] else d[i]=0 y[i]=w[i] end end
The linear expression of the above constraint can be expressed as follows:
Max $ 40𝑥+15𝑦_1−30𝑑_1+15𝑦_2−30𝑑_2+15𝑦_3−30𝑑_3$
$ x_i – y_i <= d_i, i=1:3$
$ y_i = w_i , i=1:3$
$ 0 <= x <= 5$
$ y,d_i>= 0, i=1:3$
However, I want to change the conditional constraint as follows:
for i=1:3 if w[i]-x <=0 d[i]=x-w[i]; y[i]= w[i] else d[i]=0 y[i]=x % The change end end
How can I modify the linear optimization problem to satisfy the new condition?!