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Discrete optimization is a branch of optimization in
applied mathematics Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathemat ...
and
computer science Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to practical disciplines (includin ...
.


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

Three notable branches of discrete optimization are:. * combinatorial optimization, which refers to problems on
graph Graph may refer to: Mathematics *Graph (discrete mathematics), a structure made of vertices and edges **Graph theory, the study of such graphs and their properties *Graph (topology), a topological space resembling a graph in the sense of discre ...
s, matroids and other discrete structures * integer programming *
constraint programming Constraint programming (CP) is a paradigm for solving combinatorial problems that draws on a wide range of techniques from artificial intelligence, computer science, and operations research. In constraint programming, users declaratively state th ...
These branches are all closely intertwined however since many combinatorial optimization problems can be modeled as integer programs (e.g.
shortest path In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized. The problem of finding the shortest path between t ...
) 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.


See also

* Diophantine equation


References

{{Authority control Mathematical optimization