ConstraintsInAMPL < OpsRes

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---+<a name="top"></a> Constraints in AMPL

   1 [[#describe][Description]]
   1 [[#define][Defining a Constraint]]
   1 [[#bounded][Bounded Constraints]]
   1 [[#examine][Examining Constraints]]
   1 [[#change][Changing Constraints]]

---++<a name="describe"></a> Description

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

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---++<a name="define"></a> Defining a Constraint

Constraints are defined using the =subject to= keywords, a label and possibly and indexing set, the =:= operator, two [[ExpressionsInAMPL][expressions]] and a [[LogicInAMPL][relational operator]]:
<pre>
subject to &lt;conname&gt; [{conset}] :
  &lt;lhs_expression&gt; &lt;relational operator&gt; &lt;rhs_expression&gt;;
</pre>

---+++ Examples
<pre>
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];
</pre>

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---++<a name="bounded"></a> 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.)
<pre>
subject to MeetRequirement {r in REQUIREMENTS}:
  Min[r] <= sum {i in INGREDIENTS} Contributes[i, r] * Amount[i] <= Max[r];
</pre>

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---++<a name="examine"></a> Examining Constraints

We have already seen how to observe the value of variables using [[Variables in AMPL#examine][<tt>display &lt;varname&gt;;</tt>]]. For constraints, we can look at the value of the expression involving the variables (known as the _body_) by using
<pre>
display &lt;conname&gt;.body;
</pre>

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
<pre>
expand &lt;conname&gt;;
</pre>

<img src="%ATTACHURLPATH%/examine_constraint.jpg" alt="examine_constraint.jpg" width='669' height='302' />

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---++<a name="change"></a>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.
<pre>
drop &lt;conname&gt;;
</pre>
If you decide to reinstate the constraint, you can restore it. To restore a constraint, use the =restore= keyword and the constraint name.
<pre>
restore &lt;conname&gt;;
</pre>

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-- Main.MichaelOSullivan - 02 Mar 2008
Topic revision: r1 - 2008-03-02 - MichaelOSullivan