Re: [Help-glpk] forall and exists?

[Michael Hennebry]

On Tue, 7 May 2013, Jeffrey Kantor wrote:

> Also note that the "Big M" technique commonly used to implement logical
> constraints as an MILP needs to be 'tuned' to work effectively. A proper
> value of M is data dependent, so the automatic translation of logical
> constraints to an MILP is not a trivial issue.

H[*] parameters given by problem
for some j in S, X[j]<=H[j]

b[*] added binary variables
SUM b[j] = 1
j in S

M[*] parameters to be selected
for all j in S, X[j]<=H[j]+(1-b[j])*M[j]

Select M[*] so that
for all j, b[j]==0 -> X[j]<=H[j]+M[j]

M[j]==max(X[j])-H[j] is valid, but sometimes smaller values are available.

--
Michael   address@hidden
"On Monday, I'm gonna have to tell my kindergarten class,
whom I teach not to run with scissors,
that my fiance ran me through with a broadsword."  --  Lily