Originally posted by: SystemAdmin

[ArushGadkar said:]

Hello All,
I have a variable binary vector lets say U[5]. I have a variable integer vector lets say S[5]. The constraint i am trying to formulate is as follows:

sum over all j ----> U[j]*S[j] <= C (some fixed integer) .<br />
Example if U[5] = [ 1, 1, 0 , 0, 1] then i want to formulate the constraint S[1] + S[2] + S[5] <= C.<br />
Your help is very much appreciated.
Thanks
Arush.
#DecisionOptimization
#MathematicalProgramming-General

Originally posted by: SystemAdmin

[soub said:]

Arush, just in the case that you did not find the solution....

For S \geq 0, with dim(S)=N, lets define the auxiliary continuous variable vector A, 0 \leq A.
And let M \geq UpperBound(S), a big real vector of constants. Then you can create these constraints,

1) for every i in N, 0 \leq A_i

2) for every i in N, A_i \leq M_i * U_i

3) for every i in N, 0 \leq S_i - A_i

4) for every i in N, S_i - A_i \leq M_i * (1 - U_i)

5) sum_{i in N} ( A_i ) \leq C

You can also use indicator constraints to avoid big-M constants.

Best Regards, Soub
#DecisionOptimization
#MathematicalProgramming-General

Originally posted by: SystemAdmin

[ArushGadkar said:]

Hi ,
Thanks for your help. I was able to get it though. I am actually interested in formulating the constraints depending if they form a maximal Clique. Could you read my newer post and see if you can get that. I am having troubles with it.
Thanks
Arush.
#DecisionOptimization
#MathematicalProgramming-General