Logical operators

[Dilip Kothari]

Hi
Is AMPL permit the use of logical operators.
e.g I wish to write
zn[i,j] = z[i,j] OR y[i,j]
where zn,z and y are variables. i and j are index over sets
I and J respectively.
Thanks,
DK

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[Robert Fourer]

AMPL does allow constraints that use logical operators like "or" (not "OR"),
but currently none of the AMPL-solver interfaces are set up to use such
constraints.

Bob Fourer
4...@ampl.com

[Jen T]

I'm new to AMPL, so try to forgive me if this question is posed elsewhere,
or if there is an obvious solution.

As the solvers don't support logical operators, is there an alternative way
to
encode a constraint of the following form...

subject to constraintName : c1 or c2;

... where c1 and c2 are simple non-strict inequalities?

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[Robert Fourer]

To express such a "disjunctive" constraint of this kind for current solvers,
you need to define a zero-one (or "binary") variable and to create two
constraints. The first constraint is equivalent to c1 when the binary
variable is 1, but is trivially satisfied when the binary variable is 0; the
second constraint is equivalent to c2 when the binary variable is 0, but is
trivially satisfied when the binary variable is 1.

The details depend on the specifics of your constraints. But as a simple
example if you want to specify

param a >= 0;
param b >= 0;

var x >= 0;
var y >= 0;

subj to eitheror: x >= a or y >= b;

then you can write

var u binary;

subj to eitherx: x >= a * u;
subj to eithery: y >= b * (1-u);

For other kinds of inequalities the formulation is a little different, but
it's not hard to find once you appreciate the principle involved.

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[Jen T]

Thank you!

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