Discrete optimization

Discrete optimization is a branch of optimization in applied mathematics and computer science.

Scope

As opposed to continuous optimization, some or all of the variables used in a discrete mathematical program are restricted to be discrete variables—that is, to assume only a discrete set of values, such as the integers.

Branches

Two notable branches of discrete optimization are:

• combinatorial optimization, which refers to problems on graphs, matroids and other discrete structures
• integer programming

These branches are closely intertwined however since many combinatorial optimization problems can be modeled as integer programs (e.g. shortest path) and conversely, integer programs can often be given a combinatorial interpretation.

See also

• Diophantine equation