The "level" refers to sets of variables. A bilevel program has two sets:

min f(x, y): x in X, y in Y, h(x, y)=0, g(x, y)=0.
A reason for identifying levels is to apply a decomposition principle for algorithm design. One example is the bilinear program

Bilinear program

In mathematics, a bilinear program is a nonlinear optimization problem whose objective and/or constraint functions are bilinear. An example is the pooling problem.-References:* at the Mathematical Programming Glossary....

. Another is the bilevel program

Bilevel program

In mathematics, bilevel programs are optimization problems where one optimization problem is embedded in another one.Bilevel programs are multilevel programs with two levels.- Mathematical formulation of the problem :...

 when one set of variables is constrained to be a solution to an inner optimization problem:

min f(x, y): x in X, y in Y, h(x, y)=0, g(x, y)=0, y in argmax{F(x, y): y in S(x)},
where S(x) is some subset of Y.



This topic relates to the field of Mathematical programming

Mathematical Programming

Mathematical Programming, established in 1971, and published by Springer Science+Business Media, is the official scientific journal of the Mathematical Optimization Society. It currently consists of two series: A and B. The "A" series contains general publications. The "B" series focuses on topical...

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