# Constraints in AMPL

- Description
- Defining a Constraint
- Bounded Constraints
- Examining Constraints
- Changing Constraints

## Description

Mathematical programmes use constraints to describe the relationships that define a *feasible* set of decision variables.

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## Defining a Constraint

Constraints are defined using the `subject to`

keywords, a label and possibly and indexing set, the `:`

operator, two expressions and a relational operator:

subject to <conname> [{conset}] :
<lhs_expression> <relational operator> <rhs_expression>;

### Examples

subject to LimitedResin:
sum {s in SURFBOARDS} Resin[s] * Production[s] <= TotalResin;
# Must conserve flow in the network (steel cannot disappear!)
subject to ConserveFlow {n in NODES}:
sum {m in NODES: (m, n) in ARCS} Shipment[m, n] + Supply[n] =
sum {p in NODES: (n, p) in ARCS} Shipment[n, p] + Demand[n] + Storage[n];

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## Bounded Constraints

AMPL also allows

*bounded* constraints to be defined. These constraints consist of an expression and a lower and upper bound. The lower and upper bounds may also be expressions, but

**may only involve parameters**. (

**Note** Regular constraints may have variables in either the left- or right-hand-side expressions.)

subject to MeetRequirement {r in REQUIREMENTS}:
Min[r] <= sum {i in INGREDIENTS} Contributes[i, r] * Amount[i] <= Max[r];

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## Examining Constraints

We have already seen how to observe the value of variables using `display <varname>;`. For constraints, we can look at the value of the expression involving the variables (known as the *body*) by using

display <conname>.body;

For bound constraints this represents the expression in the middle, for other constraints this represents the value of the constraint expression with all variables shifted to the left-hand side. You can see the constraints in modified form by using

expand <conname>;

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## Changing Constraints

Once constraints have been added to a model you cannot remove them. However, you can drop a given constraint from the model. To drop a constraint, use the `drop`

keyword and the constraint name.

drop <conname>;

If you decide to reinstate the constraint, you can restore it. To restore a constraint, use the

`restore`

keyword and the constraint name.

restore <conname>;

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-- MichaelOSullivan - 02 Mar 2008