discrete optimization
{{Short description|Branch of mathematical optimization}}
Discrete optimization is a branch of optimization in applied mathematics and computer science. As opposed to continuous optimization, some or all of the variables used in a discrete optimization problem are restricted to be discrete variables—that is, to assume only a discrete set of values, such as the integers.{{citation|title=A First Course in Combinatorial Optimization|volume=36|series=Cambridge Texts in Applied Mathematics|first=Jon|last=Lee|publisher=Cambridge University Press|year=2004|isbn=9780521010122|page=1|url=https://books.google.com/books?id=3pL1B7WVYnAC&pg=PA1}}.
Branches
Three notable branches of discrete optimization are:{{citation
| last1 = Hammer | first1 = P. L.
| last2 = Johnson | first2 = E. L.
| last3 = Korte | first3 = B. H.
| contribution = Conclusive remarks
| pages = 427–453
| publisher = Elsevier
| series = Annals of Discrete Mathematics
| title = Discrete Optimization II
| volume = 5
| year = 2000}}.
- combinatorial optimization, which refers to problems on graphs, matroids and other discrete structures
- integer programming
- constraint programming
These branches are all closely intertwined however, since many combinatorial optimization problems
can be modeled as integer programs (e.g. shortest path) or constraint programs,
any constraint program can be formulated as an integer program and vice versa,
and constraint and integer programs can often be given a combinatorial interpretation.