Linear Optimization with (related) multiple constraints

[Sebastian Geiger]

Dear all,

While I am using Stata for many years I have never really worked with Mata. Now, I try to set up a linear optimization model for the first time. Despite reading through the manual, I am running into some (probably beginner's) questions.

The (simplfied) model set-up is as follows:

Objective funtion:
min(r_x1 * ∆ x1 + r_x2 * ∆ x2 - r_x3 * ∆x3)

Constraints:
∆x1 + ∆x2 + ∆x3 = ∆y
-∆x1 <= x1
-∆x2 <= x2
-∆x3 <= x3
∆x1 <= a
∆x1 + ∆x2 <= b
L <= U - ∆x1 - ∆x2 + ∆y

I started with programming this:

d_y = st_data(., ("d_y"))          

x1 = st_data(., ("x1"))        
x2 = st_data(., ("x2"))       
x3 = st_data(., ("x3"))          

r_x1 = st_data(., ("r_x1"))
r_x2 = st_data(., ("r_x2"))
r_x3 = st_data(., ("r_x3"))

b = st_data(., ("a))       
a = st_data(., ("b"))      

// Objective function
c = (r_x1, r_x2, -r_x3)

// Restrictions
Aec = (1 + 1 + 1)            
bec = (d_y)

// Bounds
lowerbd = (-x1, -x2, -x3)   
upperbd = ????

The struggle begins for me already when I have multiple restrictions for the same variable.

For now i have in particular the following questions:

1. How do I define multiple constraints for the same variable? Do I use the J(.,.) function for that?
2. How can I refer to other variables within the constraint of another variable? This would be necessary for ∆x1 + ∆x2 + ∆x3 = ∆y

Any other comments or recommendations are also welcome.

Thank you!

Best wishes,
Sebastian

[Sebastian Geiger]

In question 2. im meant the way to solve the inequality contraints ∆x1 + ∆x2 <= b of course. Sorry for the confusion.

[Jared Greathouse]

You'll need to give a minimal worked example. Maybe a simple dataset to illustrate what you want Mata to produce