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.[1]

Branches

Three notable branches of discrete optimization are:[2]

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.

gollark: But the search isn't necessarily limited to usernames or channels.
gollark: You would become a tencksr, which sounds silly.
gollark: The existing system probably isn't because inverted index.
gollark: The *bigger* problem is that without some very clever engineering the time would be linear *in the number of messages*.
gollark: Search is a Hard Problem™ and it's hardly Discord's core business.

See also

References
  1. Lee, Jon (2004), A First Course in Combinatorial Optimization, Cambridge Texts in Applied Mathematics, 36, Cambridge University Press, p. 1, ISBN 9780521010122.
  2. Hammer, P. L.; Johnson, E. L.; Korte, B. H. (2000), "Conclusive remarks", Discrete Optimization II, Annals of Discrete Mathematics, 5, Elsevier, pp. 427–453.
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