As domain reduction weights more in the algorithm, it is necessary to have an efficient method to validate a variable's bound contraction implementation. Like we test strong duality during Bender's implementation, can there be a numerical method to validate any algorithm's resulting bounds?
For example, with the linear following constraints,
0.1 <= x[i] <= 3, i=1..3
x[1] + x[2] + x[3] <= 3
It is clear that 0.1 <= x[i] <= 2.8, which can be concluded using domain reduction schemes.
Say f(x) => LB(x) & UB(x), where f(x) only focus on linear constraints, how should I validate the correctness of f(x) given existing problem information.
kaarthiksundar
commented
5 years ago
As domain reduction weights more in the algorithm, it is necessary to have an efficient method to validate a variable's bound contraction implementation. Like we test strong duality during Bender's implementation, can there be a numerical method to validate any algorithm's resulting bounds?
For example, with the linear following constraints, 0.1 <= x[i] <= 3, i=1..3 x[1] + x[2] + x[3] <= 3 It is clear that 0.1 <= x[i] <= 2.8, which can be concluded using domain reduction schemes.
Say f(x) => LB(x) & UB(x), where f(x) only focus on linear constraints, how should I validate the correctness of f(x) given existing problem information.