BookmarkSubscribeRSS Feed
gupta_shubham
Obsidian | Level 7

Hi,

 

I want to use something similar to Heaviside function to create a unit pulse. Unit pulse is required because I want to define some objective function and constraint which are piece-wise linear. For example from x=0 to 10, y=x , x>=10 , y=20-x. I am unable to find out a function which could help me to write such formulation without having to write multiple if-else statement. 

 

 

3 REPLIES 3
RobPratt
SAS Super FREQ

Does your x variable have an upper bound?  Is the rest of your optimization model linear?

gupta_shubham
Obsidian | Level 7

Ideally I don't want to have any upper bound on x. Lower bound is x>0. Also my whole optimization has non linear constraints and objective function but I can simple approximated version with linear constraints 

RobPratt
SAS Super FREQ

If y - x is in [-M_1,M_1] and y - (20 - x) is in [-M_2,M_2] for suitably chosen constants M_1 and M_2, you can linearize the relationship between x and y by introducing a binary variable z and the following constraints:

-M_1 * z <= y - x <= M_1 * z

-M_2 * (1 - z) <= y - (20 - x) <= M_2 * (1 - z)

 

If z = 0, the first pair of constraints force y = x.  If z = 1, the second pair of constraints force y = 20 - x.

 

Depending on your objective and other constraints, you might be able to avoid the bounds and binary variables.  For example, if you want to maximize y, you can just impose y <= x and y <= 20 - x.

hackathon24-white-horiz.png

The 2025 SAS Hackathon Kicks Off on June 11!

Watch the live Hackathon Kickoff to get all the essential information about the SAS Hackathon—including how to join, how to participate, and expert tips for success.

YouTube LinkedIn

Discussion stats
  • 3 replies
  • 1224 views
  • 0 likes
  • 2 in conversation