mathematical optimization - Linear constraint with a floor function in Gurobi -

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i building milp constraint system. following constraint need build.

floor(a-b) <= 2c - 1

here, , b real-valued. c integer variable. need floor function able assign appropriate values variables. how add constraint in gurobi? appreciated.

assume bounded constant maxa , similarilily let b <= maxb. then, use inequalities

(1): < b + c*maxa

(2): b <= + (1-c)*maxb.

let a>=b, (1) implies c=1, , (2) trivially satisfied, independent on c. otherwise, assume less b , (2) implies c=0 , (1) becomes trivial. (you should skip (2), if want assure a>=b implies c=1, , not care c otherwise.)


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