In continuous optimization, the variables in the model are allowed to take on any value within a range of values, usually real numbers. This property of the variables is in contrast to discrete optimization, in which some or all of the variables may be binary (restricted to the values 0 and 1), integer (for which only integer values are allowed), or more abstract objects drawn from sets with finitely many elements.
An important distinction in continuous optimization is between problems in which there are no constraints on the variables and problems in which there are constraints on the variables. Unconstrained optimization problems arise directly in many practical applications; they also arise in the reformulation of constrained optimization problems in which the constraints are replaced by a penalty term in the objective function. Constrained optimization problems arise from applications in which there are explicit constraints on the variables. There are many subfields of constrained optimization for which specific algorithms are available.
The following topics are covered in other sections of the NEOS Optimization Guide.
- Unconstrained Optimization
- Constrained Optimization