Generalized semi-infinite programming

In mathematics, a semi-infinite programming (SIP) problem is an optimization problem with a finite number of variables and an infinite number of constraints. The constraints are typically parameterized. In a generalized semi-infinite programming (GSIP) problem, the feasible set of the parameters depends on the variables.[1]

Mathematical formulation of the problem

The problem can be stated simply as:

\min\limits_{x \in X}\;\; f(x)
\mbox{subject to: }\
g(x,y) \le 0, \;\; \forall y \in Y(x)

where

f: R^n \to R
g: R^n \times R^m \to R
X \subseteq R^n
Y \subseteq R^m.

In the special case that the set :Y(x) is nonempty for all x \in X GSIP can be cast as bilevel programs (Multilevel programming).

See also

References

  1. ↑ O. Stein and G. Still, On generalized semi-infinite optimization and bilevel optimization, European J. Oper. Res., 142 (2002), pp. 444-462

External links

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