Slack Variables
Slack variables are defined to transform an inequality expression into an equality expression with an added slack variable. The slack variable is defined by setting a lower bound of zero (>0).
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Inequality Constraint Form |
x > b |
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Equality Constraint Form with Slack Variable |
x = b + slack |
Example Problem
Inequality Constraints in APM
In APMonitor Modeling Language, inequality constraints are automatically translated into equality constraints with slack variables. Slack variables can also be defined by starting a variable name with slk. When the model is parsed at run-time, any variable beginning with slk is automatically assigned a lower value of zero. Alternatively, inequality constraints will be automatically converted to equality constraints with a slack variable.
Logical Conditions in Optimization
Slack variables are also useful for optimization problems with non-smooth or discontinuous functions. The following tutorial demonstrates the use of slack variables in reformulating the ABS() function, IF statements, and others.