Discrete optimization is a branch of
optimization in
applied mathematics and
computer science.
Scope
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 real ...
, 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
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
In mathematics, a Diophantine equation is an equation, typically a polynomial equation in two or more unknowns with integer coefficients, such that the only solutions of interest are the integer ones. A linear Diophantine equation equates to a c ...
References
{{Authority control
Mathematical optimization