Discrete optimization is a branch of
optimization
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. It is generally divided into two subfiel ...
in
applied mathematics
Applied mathematics is the application of mathematics, mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and Industrial sector, industry. Thus, applied mathematics is a ...
and
computer science
Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, ...
. As opposed to
continuous optimization
Continuous optimization is a branch of optimization in applied mathematics.
As opposed to discrete optimization, the variables used in the objective function are required to be continuous variables—that is, to be chosen from a set of ...
, 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
integer
An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative in ...
s.
Branches
Three notable branches of discrete optimization are:
[.]
*
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.
See also
*
Diophantine equation
References
{{Mathematical optimization
Mathematical optimization