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・ Generation of binomial series using calculus
・ Generation of Chaos
・ Generalized Pochhammer symbol
・ Generalized Poincaré conjecture
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Generalized semi-infinite programming
・ Generalized signal averaging
・ Generalized singular value decomposition
・ Generalized spectrogram
・ Generalized star height problem
・ Generalized suffix tree
・ Generalized symmetric group
・ Generalized System of Preferences
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Generalized semi-infinite programming : ウィキペディア英語版
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.〔O. Stein and G. Still, ''On generalized semi-infinite optimization and bilevel optimization'', European J. Oper. Res., 142 (2002), pp. 444-462〕
== Mathematical formulation of the problem ==
The problem can be stated simply as:
: \min\limits_\;\; f(x)
: \mbox\
:: 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).

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