Discrete optimization
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Discrete optimization is a branch of optimization in applied mathematics and computer science.
As opposed to continuous optimization, the variables used in the objective function (or some of them) are restricted to assume only discrete values, such as the integers.
Combinatorial optimization is a branch of discrete optimization that refers to problems on graphs, matroids and other discrete structures and integer programming is another branch; these branches are closely intertwined since many combinatorial optimization problems (e.g. shortest path) can be modeled as integer programs and conversely.
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