Bilevel program
Encyclopedia
In mathematics
, bilevel programs are optimization problems where one optimization problem is embedded in another one.
Bilevel programs are multilevel programs
with two levels
http://glossary.computing.society.informs.org/second.php?page=B.html#Bilevel_program.
where
The variables z are dummy variables.
Similarly the pessimistic formulation is given by
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, bilevel programs are optimization problems where one optimization problem is embedded in another one.
Bilevel programs are multilevel programs
Multilevel programming
The "level" refers to sets of variables. A bilevel program has two sets:min f: x in X, y in Y, h=0, g=0.A reason for identifying levels is to apply a decomposition principle for algorithm design. One example is the bilinear program...
with two levels
http://glossary.computing.society.informs.org/second.php?page=B.html#Bilevel_program.
Mathematical formulation of the problem
The optimistic formulation of bilevel programs problem can be stated simply as:
where
The variables z are dummy variables.
Similarly the pessimistic formulation is given by
