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Semi-infinite programming : ウィキペディア英語版
Semi-infinite programming
In optimization theory, semi-infinite programming (SIP) is an optimization problem with a finite number of variables and an infinite number of constraints, or an infinite number of variables and a finite number of constraints. In the former case the constraints are typically parameterized.〔
*
* M. A. Goberna and M. A. López, ''Linear Semi-Infinite Optimization'', Wiley, 1998.
*

==Mathematical formulation of the problem==
The problem can be stated simply as:
: \min_\;\; f(x)
: \text\
:: g(x,y) \le 0, \;\; \forall y \in Y
where
:f: R^n \to R
:g: R^n \times R^m \to R
:X \subseteq R^n
:Y \subseteq R^m.
SIP can be seen as a special case of bilevel programs in which the lower-level variables do not participate in the objective function.

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